2020-10-19T15:55:30Zhttp://edoc.mpg.de/ac_ft_oai.ploai:edoc.mpg.de:27022009-03-166:82
Plunge waveforms from inspiralling binary black holes
Baker, John G.
Brügmann, Bernd
Campanelli, Manuela
Lousto, Carlos O.
Takahashi, Ryoji
We study the coalescence of non-spinning binary black holes from the innermost stable circular orbit down to the final single rotating black hole. We use a technique that combines the full numerical approach to solve Einstein equations, applied in the truly nonlinear regime, and linearized perturbation theory around the final distorted single black hole at later times. We compute the plunge waveforms which present a non negligible signal lasting for over $tsim 100$M showing early nonlinear ringing. We also obtain estimates of the total gravitational energy radiated during this process and the plunging time.
2001
Article
http://edoc.mpg.de/2702
Physical Review Letters, v.87, 121103 (2001)
en
oai:edoc.mpg.de:27172009-03-166:82
Black Hole Excision for Dynamic Black Holes
Alcubierre, Miguel
Brügmann, Bernd
Pollney, Denis
Seidel, Edward
We extend previous work on 3D black hole excision to the case of distorted black holes, with a variety of dynamic gauge conditions that are able to respond naturally to the spacetime dynamics. We show that the combination of excision and gauge conditions we use is able to drive highly distorted, rotating black holes to an almost static state at late times, with well behaved metric functions, without the need for any special initial conditions or analytically prescribed gauge functions. Further, we show for the first time that one can extract accurate waveforms from these simulations, with the full machinery of excision and dynamic gauge conditions. The evolutions can be carried out for long times, far exceeding the longevity and accuracy of even better resolved 2D codes. While traditional 2D codes show errors in quantities such as apparent horizon mass of over 100% by t = 100M, and crash by t = 150M, with our new techniques the same systems can be evolved for hundreds of M's in full 3D with errors of only a few percent.
2001
Article
http://edoc.mpg.de/2717
Physical Review D, v.64, 061501 (2001)
en
oai:edoc.mpg.de:27182009-03-166:82
The Lazarus project : A pragmatic approach to binary black hole
Baker, John G.
Campanelli, Manuela
Lousto, Carlos O.
We present a detailed description of techniques developed to combine 3D numerical simulations and, subsequently, a single black hole close-limit approximation. This method has made it possible to compute the first complete waveforms covering the post-orbital dynamics of a binary black hole system with the numerical simulation covering the essential non-linear interaction before the close limit becomes applicable for the late time dynamics. To determine when close-limit perturbation theory is applicable we apply a combination of invariant a priori estimates and a posteriori consistency checks of the robustness of our results against exchange of linear and non-linear treatments near the interface. Once the merically modeled binary system reaches a regime that can be treated as perturbations of the Kerr spacetime, we must approximately relate the numerical coordinates to the perturbative background coordinates. We also perform a rotation of a numerically defined tetrad to asymptotically reproduce the tetrad required in the perturbative treatment. We can then produce numerical Cauchy data for the close-limit evolution in the form of the Weyl scalar $psi_4$ and its time derivative $partial_tpsi_4$ with both objects being first order coordinate and tetrad invariant. The Teukolsky equation in Boyer-Lindquist coordinates is adopted to further continue the evolution. To illustrate the application of these techniques we evolve a single Kerr hole and compute the spurious radiation as a measure of the error of the whole procedure. We also briefly discuss the extension of the project to make use of improved full numerical evolutions and outline the approach to a full understanding of astrophysical black hole binary systems which we can now pursue.
2002
Article
http://edoc.mpg.de/2718
Physical Review D, v.65 (2002)
en
oai:edoc.mpg.de:27212009-03-166:82
Gravitational Wave Damping of Neutron Star Wobble
Cutler, Curt
Jones, David Ian
We calculate the effect of gravitational wave (gw) back-reaction on realistic neutron stars (NS's) undergoing torque-free precession. By ''realistic' we mean that the NS is treated as a mostly-fluid body with an elastic crust, as opposed to a rigid body. We find that gw's damp NS wobble on a timescale tau_{theta} approx 2 x 10^5 yr [10^{-7}/(DId/I_0)]^2 (kHz/ nu_s)^4, where nu_s is the spin frequency and DId is the piece of the NS's inertia tensor that "follows" the crust's principal axis (as opposed to its spin axis). We give two different derivations of this result: one based solely on energy and angular momentum balance, and another obtained by adding the Burke-Thorne radiation reaction force to the Newtonian equations of motion. This problem was treated long ago by Bertotti and Anile (1973), but their claimed result is wrong. When we convert from their notation to ours, we find that their tau_{theta} is too short by a factor of order 10^5 for typical cases of interest, and even has the wrong sign for DId negative. We show where their calculation went astray.
2001
Article
http://edoc.mpg.de/2721
Physical Review D, v.63, 024002 (2001)
en
oai:edoc.mpg.de:27462009-03-166:82
Gravitational self force by mode sum regularization
Barack, Leor
We propose a practical scheme for calculating the local gravitational self-force experienced by a test mass particle moving in a black hole spacetime. The method---equally effective for either weak or strong field orbits---employs the {em mode-sum regularization scheme} previously developed for a scalar toy model. The starting point for the calculation, in this approach, is the formal expression for the regularized self-force derived by Mino et al. (and, independently, by Quinn and Wald), which involves a worldline integral over the tail part of the retarded Green's function. This force is decomposed into multipole (tensor harmonic) modes, whose sum is subjected to a carefully designed regularization procedure. This procedure involves an analytic derivation of certain ''''regularization parameters'' by means of a local analysis of the Green's function. This manuscript contains the following main parts: (1) Introduction of the mode sum scheme as applied to the gravitational case. (2) Two simple cases studied: the test case of a static particle in flat spacetime, and the case of a particle at a turning point of a radial geodesic in Schwarzschild spacetime. In both cases we derive all necessary regularization parameters. (3) An Analytic foundation is set for applying the scheme in more general cases. (In this paper, the mode sum scheme is formulated within the harmonic gauge. The implementation of the scheme in other gauges shall be discussed in a separate, forthcoming paper.)
2001
Article
http://edoc.mpg.de/2746
Physical Review D, v.64, 084021 (2001)
en
oai:edoc.mpg.de:27492009-03-166:82
Gravitational self force and gauge transformations
Barack, Leor
Ori, Amos
We explore how the gravitational self force (or ''''radiation reaction'' force), acting on a pointlike test particle in curved spacetime, is modified in a gauge transformation. We derive the general transformation law, describing the change in the self force in terms of the infinitesimal displacement vector associated with the gauge transformation. Based on this transformation law, we extend the regularization prescription by Mino et al. and Quinn and Wald (originally formulated within the harmonic gauge) to an arbitrary gauge. Then we extend the method of mode-sum regularization (which provides a practical means for calculating the regularized self force and was recently applied to the harmonic-gauge gravitational self force) to an arbitrary gauge. We find that the regularization parameters involved in this method are gauge-independent. We also explore the gauge transformation of the self force from the harmonic gauge to the Regge-Wheeler gauge and to the radiation gauge, focusing attention on the regularity of these gauge transformations. We conclude that the transformation of the self force to the Regge-Wheeler gauge in Schwarzschild spacetime is regular for radial orbits and irregular otherwise, whereas the transformation to the radiation gauge is irregular for all orbits.
2001
Article
http://edoc.mpg.de/2749
Physical Review D, v.64, 124003 (2001)
en
oai:edoc.mpg.de:27562009-03-166:82
On the stability of the Kerr metric
Beyer, Horst R.
The reduced (in the angular coordinate phi) wave equation and Klein-Gordon equation are considered on a Kerr background and in the framework of C-0-semigroup theory. Each equation is shown to have a well-posed initial value problem, i.e., to have a unique solution depending continuously on the data. Further, it is shown that the spectrum of the semigroup's generator coincides with the spectrum of an operator polynomial whose coefficients can be read off from the equation. In this way the problem of deciding stability is reduced to a spectral problem and a mathematical basis is provided for mode considerations. For the wave equation it is shown that the resolvent of the semigroup's generator and the corresponding Green's functions can be computed using spheroidal functions. It is to be expected that, analogous to the case of a Schwarzschild background, the quasinormal frequencies of the Kerr black hole appear as resonances, i.e., poles of the analytic continuation of this resolvent. Finally, stability of the solutions of the reduced Klein-Gordon equation is proven for large enough masses.
2001
Article
http://edoc.mpg.de/2756
Communications in Mathematical Physics, v.221, 659-676 (2001)
en
oai:edoc.mpg.de:27652009-03-166:82
Isometric embeddings of black hole horizons in three-dimensional flat space
Bondarescu, Mihai
Alcubierre, Miguel
Seidel, Edward
The geometry of a two-dimensional surface in a curved space can be most easily visualized by using an isometric embedding in flat three-dimensional space. Here we present a new method for embedding surfaces with spherical topology in flat space when such an embedding exists. Our method is based on expanding the surface in spherical harmonics and minimizing the differences between the metric on the original surface and on the trial surface in the space of the expansion coefficients. We have applied this method to study the geometry of black-hole horizons in the presence of strong, non-axisymmetric, gravitational waves (Brill waves). We have noted that, in many cases, although the metric of the horizon seems to have large deviations from axisymmetry, the intrinsic geometry of the horizon is almost axisymmetric. The origin of the large apparent non-axisymmetry of the metric is the deformation of the coordinate system in which the metric was computed.
2002
Article
http://edoc.mpg.de/2765
Classical and Quantum Gravity, v.19, 375-391 (2002)
en
oai:edoc.mpg.de:27682009-03-166:82
Effect of hyperon bulk viscosity on neutron-star r-modes
Lindblom, Lee
Owen, Benjamin J.
Neutron stars are expected to contain a significant number of hyperons in addition to protons and neutrons in the highest density portions of their cores. Following the work of Jones, we calculate the coefficient of bulk viscosity due to nonleptonic weak interactions involving hyperons in neutron-star cores, including new relativistic and superfluid effects. We evaluate the influence of this new bulk viscosity on the gravitational radiation driven instability in the r-modes. We find that the instability is completely suppressed in stars with cores cooler than a few times 109 K, but that stars rotating more rapidly than 10?30% of maximum are unstable for temperatures around 1010 K. Since neutron-star cores are expected to cool to a few times 109 K within seconds (much shorter than the r-mode instability growth time) due to direct Urca processes, we conclude that the gravitational radiation instability will be suppressed in young neutron stars before it can significantly change the angular momentum of the star.
2002
Article
http://edoc.mpg.de/2768
Physical Review D, v.65 (2002)
en
oai:edoc.mpg.de:27692009-03-166:82
Calculating the gravitational self force in Schwarzschild spacetime
Barack, Leor
Mino, Yasushi
Nakano, Hiroyuki
Ori, Amos
Sasaki, Misao
We present a practical method for calculating the local gravitational self-force (often called "radiation-reaction force") for a pointlike particle orbiting a Schwarzschild black hole. This is an implementation of the method of mode-sum regularization, in which one first calculates the (finite) contribution to the force due to each individual multipole mode of the perturbation, and then applies a certain regularization procedure to the mode sum. Here we give the values of all the "regularization parameters" required for implementing this regularization procedure, for any geodesic orbit in Schwarzschild spacetime
2002
Article
http://edoc.mpg.de/2769
Physical Review Letters, v.88 (2002)
en
oai:edoc.mpg.de:27852009-05-276:82
Keplerian frequencies and innermost stable circular orbits of rapidly rotating strange stars
Stergioulas, Nikolaos
Kluzniak, W.
Bulik, T.
It has been suggested that the frequency in the co-rotating innermost stable circular orbit (ISCO) about a compact stellar remnant can be determined through X-ray observations of low-mass X-ray binaries, and that its value can be used to constrain the equation of state of ultradense matter.
Upon constructing numerical models of rapidly rotating strange (quark) stars in general relativity, we find that for stars rotating at the equatorial mass-shedding limit, the ISCO is indeed above the stellar surface, for a wide range of central energy densities at a height equal to 11% of the circumferential stellar radius, which scales inversely with the square root of the energy density, of self-bound quark matter at zero presure. In contrast to static stars, the ISCO frequencies of rapidly rotating strange stars can be as low as 0.9 kHz for a 1.3 solar mass strange star. Hence, the presence of strange stars in low-mass X-ray binaries cannot be excluded on the basis of the currently observed frequencies of kHz QPOs, such as the cut-off frequency of 1066 Hz in 4U 1820-30.
1999
Article
http://edoc.mpg.de/2785
Astronomy and Astrophysics, v.352, L116-L120 (1999)
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oai:edoc.mpg.de:27902009-03-166:82
Adaptive filtering techniques for gravitational wave interferometric data: Removing long-term sinusoidal disturbances and oscillatory transients
Chassande-Mottin, Eric
Dhurandhar, Sanjeev
It is known by the experience gained from the gravitational wave detector prototypes that the interferometric output signal will be corrupted by a significant amount of non-Gaussian noise, a large part of it being essentially composed of long-term sinusoids with a slowly varying envelope (such as violin resonances in the suspensions, or main power harmonics) and short-term ringdown noise (which may emanate from servo control systems, electronics in a nonlinear state, etc.). Since non-Gaussian noise components make the detection and estimation of the gravitational wave signature more difficult, a denoising algorithm based on adaptive filtering techniques (LMS methods) is proposed to separate and extract them from the stationary and Gaussian background noise. The strength of the method is that it does not require any precise model on the observed data: the signals are distinguished on the basis of their autocorrelation time. We believe that the robustness and simplicity of this method make it useful for data preparation and for the understanding of the first interferometric data. We present the detailed structure of the algorithm and its application to both simulated data and real data from the LIGO 40 m prototype.
2001
Article
http://edoc.mpg.de/2790
Physical Review D, v.63, 042004 (2001)
en
oai:edoc.mpg.de:27932009-03-166:82
Gravitational waves from black hole collisions via an eclectic approach
Baker, John G.
Brügmann, Bernd
Campanelli, Manuela
Lousto, Carlos O.
We present the first results in a new program intended to make the best use of all available technologies to provide an effective understanding of waves from inspiralling black hole binaries in time to assist imminent observations. In particular, we address the problem of combining the close-limit approximation describing ringing black holes and full numerical relativity, required for essentially nonlinear interactions. We demonstrate the effectiveness of our approach using general methods for a model problem, the head-on collision of black holes. Our method allows a more direct physical understanding of these collisions indicating clearly when non-linear methods are important. The success of this method supports our expectation that this unified approach will be able to provide relevant results for black hole binaries in time to assist gravitational wave observations.
2000
Article
http://edoc.mpg.de/2793
Classical and Quantum Gravity, v.17, L149-L156 (2000)
en
oai:edoc.mpg.de:27942009-03-166:82
Making use of geometrical invariants in black hole collisions
Baker, John G.
Campanelli, Manuela
We consider curvature invariants in the context of black hole collision simulations. In particular, we propose a simple and elegant combination of the Weyl invariants I and J, the speciality index [script S]. In the context of black hole perturbations [script S] provides a measure of the size of the distortions from an ideal Kerr black hole spacetime. Explicit calculations in well-known examples of axisymmetric black hole collisions demonstrate that this quantity may serve as a useful tool for predicting in which cases the close limit can provide an accurate estimate of the radiation wave form and energy. This makes [script S] particularly suited to studying the transition from nonlinear to linear dynamics and for an invariant interpretation of numerical results.
2000
Article
http://edoc.mpg.de/2794
Physical Review D, v.62, 127501 (2000)
en
oai:edoc.mpg.de:27962009-03-166:82
Towards a Stabel Numerical Evolution of Strongly Gravitating Systems in General Relativity :The Conformal Treatments
Alcubierre, Miguel
Brügmann, Bernd
Dramlitsch, Thomas
Font, Jose A.
Papadopoulos, Philippos
Seidel, Edward
Stergioulas, Nikolaos
Takahashi, Ryoji
We study the stability of three-dimensional numerical evolutions of the Einstein equations, comparing the standard ADM formulation to variations on a family of formulations that separate out the conformal and traceless parts of the system. We develop an implementation of the conformal-traceless (CT) approach that has improved stability properties in evolving weak and strong gravitational fields, and for both vacuum and spacetimes with active coupling to matter sources. Cases studied include weak and strong gravitational wave packets, black holes, boson stars and neutron stars. We show under what conditions the CT approach gives better results in 3D numerical evolutions compared to the ADM formulation. In particular, we show that our implementation of the CT approach gives more long term stable evolutions than ADM in all the cases studied, but is less accurate in the short term for the range of resolutions used in our 3D simulations. Š2000 The American Physical Society
2000
Article
http://edoc.mpg.de/2796
Physical Review D, v.62, 044034 (2000)
en
oai:edoc.mpg.de:28062009-03-166:82
Simple excision of a black hole in 3 + 1 numerical relativity
Alcubierre, Miguel
Brügmann, Bernd
We describe a simple implementation of black hole excision in 3 + 1 numerical relativity. We apply this technique to a Schwarzschild black hole with
octant symmetry in Eddington-Finkelstein coordinates and show how one can obtain accurate, long-term stable numerical evolutions.
2001
Article
http://edoc.mpg.de/2806
Physical Review D, v.63 (2001)
en
oai:edoc.mpg.de:28072009-03-166:82
Effect of a neutron-star crust on the r-mode instability
Lindblom, Lee
Owen, Benjamin J.
Ushomirsky, Greg
The presence of a viscous boundary layer under the solid crust of a neutron star dramatically increases the viscous damping rate of the fluid
r-modes. We improve previous estimates of this damping rate by including the effect of the Coriolis force on the boundary-layer eigenfunction and
by using more realistic neutron-star models. If the crust is assumed to be perfectly rigid, the gravitational radiation driven instability in the r-modes
is completely suppressed in neutron stars colder than about 1.5×108 K. Energy generation in the boundary layer will heat the star, and will even
melt the crust if the amplitude of the r-mode is large enough. We solve the heat equation explicitly (including the effects of thermal conduction and
neutrino emission) and find that the r-mode amplitude needed to melt the crust is alphac[approximate]5×103 for maximally rotating neutron stars.
If the r- mode saturates at an amplitude larger than alphac, the heat generated is sufficient to maintain the outer layers of the star in a mixed
fluid-solid state analogous to the pack ice on the fringes of the Arctic Ocean. We argue that in young, rapidly rotating neutron stars this effect
considerably delays the formation of the crust. By considering the dissipation in the ice flow, we show that the final spin frequency of stars with
r-mode amplitude of order unity is close to the value estimated for fluid stars without a crust.
2000
Article
http://edoc.mpg.de/2807
Physical Review D, v.62, 084030 (2000)
en
oai:edoc.mpg.de:28092009-03-176:82
Investigations of 3D binary Black Hole Systems
Nerger, Lars
Thesis
http://edoc.mpg.de/2809
en
oai:edoc.mpg.de:30312009-03-166:82
Computational cost for detecting inspiraling binaries using a network of laser interferometric detectors
Pai, Archana
Bose, Sukanta
Dhurandhar, Sanjeev
We extend a coherent network data-analysis strategy developed earlier for detecting Newtonian waveforms to the case of post-Newtonian (PN) waveforms. Since the PN waveform depends on the individual masses of the inspiralling binary, the parameter-space dimension increases by one from that of the Newtonian case. We obtain the number of templates and estimate the computational costs for PN waveforms: for a lower mass limit of I M,,, for LIGO-I noise and with 3% maximum mismatch, the online computational speed requirement for single detector is a few Gflops; for a two-detector network it is hundreds of Gflops and for a three-detector network it is tens of Tflops. Apart from idealistic networks, we obtain results for realistic networks comprising of LIGO and VIRGO. Finally, we compare costs incurred in a coincidence detection strategy with those incurred in the coherent strategy detailed above
2002
Article
http://edoc.mpg.de/3031
Classical and Quantum Gravity, v.19, 1477-1483 (2002)
en
oai:edoc.mpg.de:30322009-03-166:82
A robust and coherent network statistic for detecting gravitational waves from inspiraling compact binaries in non-Gaussian noise
Bose, Sukanta
The robust statistic proposed by Creighton and Allen et al. for
detection in stationary non-Gaussian noise is briefly reviewed.
After restoring a contribution to this statistic that was
absent in those analyses, we reinterpret the role of the
resulting robust statistic. We then obtain the analogous robust
statistic for detecting inspiral waveforms in a single detector.
We also derive the coherent statistic for detecting such signals
with an arbitrary network of earth-based interferometers.
Finally, we show that excess computational costs incurred owing
to non-Gaussianity is negligible compared to the cost of
detection in Gaussian noi
2002
Article
http://edoc.mpg.de/3032
Classical and Quantum Gravity, v.19, 1437-1442 (2002)
en
oai:edoc.mpg.de:30342009-03-166:82
On the observational determination of squeezing in relic gravitational waves and primordial density perturbations
Bose, Sukanta
Grishchuk, L. P.
We develop a theory in which relic gravitational waves and primordial density perturbations are generated by strong variable gravitational field of the
early Universe. The generating mechanism is the superadiabatic (parametric) amplification of the zero-point quantum oscillations. The generated
fields have specific statistical properties of squeezed vacuum quantum states. Macroscopically, squeezing manifests itself in a nonstationary
character of variances and correlation functions of the fields, the periodic structures of the metric power spectra, and, as a consequence, in the
oscillatory behavior of the higher order multipoles Cl of the cosmic microwave background anisotropy. We start with the gravitational wave
background and then apply the theory to primordial density perturbations. We derive an analytical formula for the positions of peaks and dips in the
angular power spectrum l(l + 1)Cl as a function of l. This formula shows that the values of l at the peak positions are ordered in the proportion
1:3:5:..., whereas at the dips they are ordered as 1:2:3:... . We compare the derived positions with the actually observed features, and find them
to be in reasonably good agreement. It appears that the observed structure is better described by our analytical formula based on the (squeezed)
metric perturbations associated with the primordial density perturbations, rather than by the acoustic peaks reflecting the existence of plasma
sound waves at the last scattering surface. We formulate a forecast for other features in the angular power spectrum that may be detected by the
advanced observational missions, such as the Microwave Anisotropy Probe and Planck. We tentatively conclude that the observed structure is a
macroscopic manifestation of squeezing in the primordial metric perturbations
2002
Article
http://edoc.mpg.de/3034
Physical Review D, v.66 (2002)
en
oai:edoc.mpg.de:30352009-03-166:82
Towards a data and detector characterization robot for gravitational wave detectors
Mohanty, Soumya
Mukherjee, Soma
A change of non-astrophysical origin in the detector state or in the statistical nature of data while an interferometer is in lock reflects an abnormality. The change can manifest itself in many forms: transients, drifts in noise power spectral density, change in cross correlation between channels, etc. We advance the idea of an algorithm for detecting such change points whose design goal is reliable performance, i.e. a known false alarm rate, even when statistically unmodelled data such as those from the physical environmental monitors are included, Reliability is important since following up on such change points could be fairly labour intensive. Such an algorithm need not be simply a collection of isolated independent monitors running in parallel. We present the first design steps towards building this detector characterization robot along with some preliminary results and outline some possibilities for the future
2002
Article
http://edoc.mpg.de/3035
Classical and Quantum Gravity, v.19, 1471-1476 (2002)
en
oai:edoc.mpg.de:30492009-03-176:82
Results on the spectrum of R-Modes of slowly rotating relativistic stars
Beyer, Horst R.
The paper considers the spectrum of axial perturbations of slowly uniformly rotating general relativistic stars in the framework of Y. Kojima. In a first step towards a full analysis only the evolution equations are treated but not the constraint. Then it is found that the system is unstable due to a continuum of non real eigenvalues. In addition the resolvent of the associated generator of time evolution is found to have a special structure which was discussed in a previous paper. From this structure it follows the occurrence of a continuous part in the spectrum of oscillations at least if the system is restricted to a finite space as is done in most numerical investigations. Finally, it can be seen that higher order corrections in the rotation frequency can qualitatively influence the spectrum of the oscillations. As a consequence different descriptions of the star which are equivalent to first order could lead to different results with respect to the stability of the star
2002
Article
http://edoc.mpg.de/3049
en
oai:edoc.mpg.de:30702009-03-166:82
Scalar Field Dark Matter and Galaxy Formation
Alcubierre, Miguel
Guzman, F. Siddhartha
Matos, Tonatiuh
Nunez, Dario
Urena-Lopez, L. Arturo
Wiederhold, Petra
We present a general description of the scalar field dark matter (SFDM) hypothesis in the cosmological context. The scenario of structure formation under such a hypothesis is based on Jeans instabilities of fluctuations of the scalar field. It is shown that it is possible to form stable long lived objects consisting of a wide range of typical galactic masses around $10^{12}M_{odot}$ once the parameters of the effective theory are fixed with the cosmological constraints. The energy density at the origin of such an object is smooth as it should
Springer
2002
Conference-Paper
http://edoc.mpg.de/3070
urn:ISSN:3-540-44257-X
Klapdor-Kleingrothaus, Hans Volker: Dark matter in astro- and particle physics : proceedings of the international conference, DARK 2002, Cape Town, South Africa, 4-9 February 2002, Springer (2002)
en
oai:edoc.mpg.de:30752009-03-176:82
Gauge conditions for long-term numerical black hole evolutions without excision
Alcubierre, Miguel
Brügmann, Bernd
Diener, Peter
Koppitz, Michael
Pollney, Denis
Seidel, Edward
Takahashi, Ryoji
Numerical relativity has faced the problem that standard 3+1 simulations without black hole excision and with singularity avoiding lapse and vanishing shift fail after an evolution time of around 30-40M due to the so-called grid stretching. We discuss lapse and shift conditions for the non-excision case that effectively cure grid stretching and allow run times of 500M and more.
2003
Article
http://edoc.mpg.de/3075
Physical Review D, v.67 (2003)
en
oai:edoc.mpg.de:30762009-03-166:82
Regularization parameters for the self force in Schwarzschild spacetime: 1. scalar case
Barack, Leor
Ori, Amos
We derive the explicit values of all regularization parameters (RP) for a scalar particle in an arbitrary geodesic orbit around a Schwarzschild black hole. These RP are required within the previously introduced mode-sum method for calculating the local self-force acting on the particle. In this method, one first calculates the (finite) contribution to the self-force due to each individual multipole mode of the particle's field, and then applies a certain regularization procedure to the mode sum, involving the RP. The explicit values of the RP were presented in a recent paper [L. Barack et al., Phys. Rev. Lett. 88, 091101 (2002)]. Here we give the full details of the RP derivation in the scalar case. The calculation of the RP in the electromagnetic and gravitational cases will be discussed in an accompanying paper
2002
Article
http://edoc.mpg.de/3076
Physical Review D, v.66 (2002)
en
oai:edoc.mpg.de:30772009-03-166:82
Computing the gravitational self-force on a compact object plunging into a Schwarzschild black hole
Barack, Leor
Lousto, Carlos O.
We compute the gravitational self-force (or "radiation reaction" force) acting on a particle falling radially into a Schwarzschild black hole. Our calculation is based on the "mode-sum" method, in which one first calculates the individual l-multipole contributions to the self-force (by numerically integrating the decoupled perturbation equations) and then regularizes the sum over modes by applying a certain analytic procedure. We demonstrate the equivalence of this method with the zeta-function scheme. The convergence rate of the mode-sum series is considerably improved here (thus reducing computational requirements) by employing an analytic approximation at large l
2002
Article
http://edoc.mpg.de/3077
Physical Review D, v.66 (2002)
en
oai:edoc.mpg.de:30822009-03-166:82
Optimal Strategies for sinusoidal signal detection
Allen, Bruce
Papa, Maria Alessandra
Schutz, Bernard F.
We derive and study optimal and nearly-optimal strategies for the detection of sinusoidal signals hidden in additive (Gaussian and non-Gaussian) noise. Such strategies are an essential part of algorithms for the detection of the gravitational Continuous Wave signals produced by pulsars. Optimal strategies are derived for the case where the signal phase is not known and the product of the signal frequency and the observation time is non-integral.
2002
Article
http://edoc.mpg.de/3082
Physical Review D, v.66 (2002)
en
oai:edoc.mpg.de:30862009-03-176:82
Binary black hole initial data for numerical general relativity based on post-Newtonian data
Tichy, Wolfgang
Brügmann, Bernd
Campanelli, Manuela
Diener, Peter
With the goal of taking a step toward the construction of astrophysically realistic initial data for numerical simulations of black holes, we for the first time derive a family of fully general relativistic initial data based on post-2-Newtonian expansions of the 3-metric and extrinsic curvature without spin. It is expected that such initial data provide a direct connection with the early inspiral phase of the binary system. We discuss a straightforward numerical implementation, which is based on a generalized puncture method. Furthermore, we suggest a method to address some of the inherent ambiguity in mapping post-Newtonian data onto a solution of the general relativistic constraints
2003
Article
http://edoc.mpg.de/3086
Physical Review D, v.67 (2003)
oai:edoc.mpg.de:31012009-03-166:82
Numerical evidence for multi-scalar stars
Hawley, Scott H.
Choptuik, Matthew W.
We present a class of general relativistic soliton-like solutions composed of multiple minimally coupled, massive, real scalar fields which interact only through the gravitational field. We describe a two-parameter family of solutions we call ''''phase-shifted boson stars (parameterized by central density $
ho_0$ and phase $delta$), which are obtained by solving the ordinary differential equations associated with boson stars and then altering the phase between the real and imaginary parts of the field. These solutions are similar to boson stars as well as the oscillating soliton stars found by Seidel and Suen [E. Seidel and W.~M. Suen, Phys. Rev. Lett. { f 66}, 1659 (1991)]; in particular, long-time numerical evolutions suggest that phase-shifted boson stars are stable. Our results indicate that scalar soliton-like solutions are perhaps more generic than has been previously thought
2003
Article
http://edoc.mpg.de/3101
Physical Review D, v.67 (2003)
en
oai:edoc.mpg.de:31062009-03-166:82
Geometric Characterizations of the Kerr Isolated Horizon
Lewandowski, Jerzy
Pawlowski, Tomasz
We formulate conditions on the geometry of a nonexpanding horizon Delta which axe sufficient for the spacetime metric to coincide on Delta with the Kerr metric. We introduce an invariant which can be used as a measure of how different the geometry of a given nonexpanding horizon is from the geometry of the Kerr horizon. Directly, our results concern the spacetime metric at Delta at the zeroth and the first orders. Combined with the results of Ashtekar, Beetle and Lewandowski, our conditions can be used to compare the spacetime geometry at the nonexpanding horizon with that of Kerr to every order. The results should be useful to numerical relativity in analyzing the sense in which the final black hole horizon produced by a collapse or a merger approaches the Kerr horizon.
2002
Article
http://edoc.mpg.de/3106
International Journal of Modern Physics D, v.11, 739-746 (2002)
en
oai:edoc.mpg.de:31132009-03-166:82
Regularization parameters for the self force in Schwarzschild spacetime: 2. gravitational and electromagnetic cases
Barack, Leor
Ori, Amos
We obtain all ''''regularization parameters'' (RP) needed for calculating the gravitational and electromagnetic self forces for an arbitrary geodesic orbit around a Schwarzschild black hole. These RP values are required for implementing the previously introduced mode-sum method, which allows a practical calculation of the self force by summing over contributions from individual multipole modes of the particle's field. In the gravitational case, we provide here full details of the analytic method and results briefly reported in a recent Letter [Phys. Rev. Lett. { f 88}, 091101 (2002)]. In the electromagnetic case, the RP are obtained here for the firs
2003
Article
http://edoc.mpg.de/3113
Physical Review D, v.67 (2003)
en
oai:edoc.mpg.de:31202009-03-176:82
Gravity, torsion, Dirac field and computer algebra using MAPLE and REDUCE
Vulcanov, Dumitru N.
The article presents computer algebra procedures and routines applied to the study of the Dirac field on curved spacetimes. The main part of the procedures is devoted to the construction of Pauli and Dirac matrices algebra on an anholonomic orthonormal reference frame. Then these procedures are used to compute the Dirac equation on curved spacetimes in a sequence of special dedicated routines. A comparative review of such procedures obtained for two computer algebra platforms (REDUCE + EXCALC and MAPLE + GRTensorII) is carried out. Applications for the calculus of the calculus of Dirac equation on specific examples of spacetimes with or without torsion are pointed out
2002
Article
http://edoc.mpg.de/3120
Computer Physics Communications (2002)
oai:edoc.mpg.de:31212009-03-176:82
Doing numerical cosmology with the Cactus code
Vulcanov, Dumitru N.
The article presents some aspects concerning the construction of a new thorn for the Cactus code, a complete 3-dimensional machinery for numerical relativity. This thorn is completely dedicated to numerical simulations in cosmology, that means it can provide evolutions of different cosmological models, mainly based on Friedman-Robertson-Walker metric. Some numerical results are presented, testing the convergence, stability and the applicability of the code.
2002
Article
http://edoc.mpg.de/3121
Computer Physics Communications (2002)
en
oai:edoc.mpg.de:31222009-03-166:82
Extremal Isolated Horizons: A Local Uniqueness Theorem
Lewandowski, Jerzy
Pawlowski, Tomasz
We derive all the axi-symmetric, vacuum, and electrovac extremal isolated horizons. It turns out, that for every horizon in this class, the induced metric tensor, the rotation 1-form potential, and the pullback of the electromagnetic field necessarily coincide with those induced by the monopolar, extremal Kerr-Newman solution on the event horizon. We also discuss the general case of a symmetric, extremal isolated horizon. In particular, we analyze the case of a 2-dimensional symmetry group generated by two null vector fields. Its relevance to the classification of all the symmetric isolated horizons, including the non-extremal once, is explained.
2003
Article
http://edoc.mpg.de/3122
Classical and Quantum Gravity, v.20, 587-606 (2003)
en
oai:edoc.mpg.de:31232009-04-066:82
Fractional Calculus via Functional Calculus: Theory and Applications
Kempfle, Siegmar
Schäfer, Ingo
Beyer, Horst
This paper demonstrates the power of the functional-calculus definition of linear fractional (pseudo-)differential operators via generalised Fourier transforms. Firstly, we describe in detail how to get global causal solutions of linear fractional differential equations via this calculus. The solutions are represented as convolutions of the input functions with the related impulse responses. The suggested method via residue calculus separates an impulse response automatically into an exponentially damped (possibly oscillatory) part and a ''slow' relaxation. If an impulse response is stable it becomes automatically causal, otherwise one has to add a homogeneous solution to get causality. Secondly, we present examples and, moreover, verify the approach along experiments on viscolelastic rods. The quality of the method as an effective few-parameter model is impressively demonstrated: the chosen reference example PTFE (Teflon) shows that in contrast to standard classical models our model describes the behaviour in a wide frequency range within the accuracy of the measurement. Even dispersion effects are included. Thirdly, we conclude the paper with a survey of the required theory. There the attention is directed to the extension from the L-2-approach on the space of distributions cal D-'
2002
Article
http://edoc.mpg.de/3123
Nonlinear Dynamics, v.29, 99-127 (2002)
en
oai:edoc.mpg.de:31392009-04-066:82
The oscillation and stability of differentially rotating spherical shells
Watts, Anna L.
Andersson, Nils
Beyer, Horst
Schutz, Bernard F.
An understanding of the dynamics of differentially rotating systems is key to many areas of astrophysics. We investigate the oscillations of a simple system exhibiting differential rotation, and discuss issues concerning the role of corotation points and the emergence of dynamical instabilities. This problem is of particular relevance to the emission of gravitational waves from oscillating neutron stars, which are expected to possess significant differential rotation immediately after birth or binary merger.
2003
Article
http://edoc.mpg.de/3139
Monthly Notices of the Royal Astronomical Society, v.342, 1156-1168 (2003)
en
oai:edoc.mpg.de:31402009-03-166:82
Texture-based volume rendering of adaptive mesh refinement data
Kähler, Ralf
Hege, Hans-Christian
Many phenomena in nature and engineering happen simultaneously on rather diverse spatial and temporal scales. In other words, they exhibit a multi-scale character. A special numerical multilevel technique associated with a particular hierarchical data structure is adaptive mesh refinement (AMR). This scheme achieves locally very high spatial and temporal resolutions. Due to its popularity, many scientists are in need of interactive visualization tools for AMR data. In this article, we present a 3D texture-based volume-rendering algorithm for AMR data that directly utilizes the hierarchical structure. Thereby fast rendering performance is achieved even for high-resolution data sets. To avoid multiple rendering of regions that are covered by grids of different levels of resolution, we propose a space partitioning scheme to decompose the volume into axis-aligned regions of equal-sized cells. Furthermore the problems of interpolation artifacts, opacity corrections, and texture memory limitations are addressed.
2002
Article
http://edoc.mpg.de/3140
The Visual Computer, v.18, 481-492 (2002)
en
oai:edoc.mpg.de:31762009-03-166:82
Gravitational self-force on a particle orbiting a Kerr black hole
Barack, Leor
Ori, Amos
We present a practical method for calculating the gravitational self-force, as well as the electromagnetic and scalar self forces, for a particle in a generic orbit around a Kerr black hole. In particular, we provide the values of all the regularization parameters needed for implementing the (previously introduced) {it mode-sum regularization} method. We also address the gauge-regularization problem, as well as a few other issues involved in the calculation of gravitational radiation-reaction in Kerr spacetime.
2003
Article
http://edoc.mpg.de/3176
Physical Review Letters, v.90 (2003)
en
oai:edoc.mpg.de:31832009-03-166:82
Removing Line Interference from Gravitational Wave Interferometer Data
Sintes, Alicia M.
Schutz, Bernard F.
We describe a procedure to identify and remove a class of interference lines from gravitational wave interferometer data. We illustrate the usefulness of this technique applying it to prototype interferometer data and removing all those lines corresponding to the external electricity main supply and related features.
Frontiers Science Series n. 32; Universal Academy Press, Inc.
2001
Conference-Paper
http://edoc.mpg.de/3183
Kawamura, S.; Mio, N.: Proceedings of 2nd TAMA Workshop on Gravitational Wave detection, Frontiers Science Series n. 32; Universal Academy Press, Inc., 273-278 (2001)
en
oai:edoc.mpg.de:32082009-03-166:82
Gravitational Radiation
Schutz, Bernard F.
Gravity is one of the fundamental forces of Nature, and it is the dominant force in most astronomical systems. In common with all other phenomena, gravity must obey the principles of special relativity. In particular, gravitational forces must not be transmitted or communicated faster than light. This means that when the gravitational field of an object changes, the changes ripple outwards through space and take a finite time to reach other objects. These ripples are called gravitational radiation or gravitational waves. This article gives a brief introduction to the physics of gravitational radiation, including technical material suitable for non-specialist scientists.
Institute of Physics Publishing / Nature Publishing Group
2001
InBook
http://edoc.mpg.de/3208
info:doi/10.1888/0333750888/2110
Encyclopedia of Astronomy and Astrophysics Vol.2, 1030-1042 (2001)
en
oai:edoc.mpg.de:32152009-03-176:82
A framework for perturbations and stability of differentially rotating stars
Beyer, Horst R.
The paper provides a new framework for the description of linearized adiabatic lagrangian perturbations and stability of differentially rotating newtonian stars. In doing so it overcomes problems in a previous framework by Dyson and Schutz and provides the basis of a rigorous analysis of the stability of such stars. For this the governing equation of the oscillations is written as a first order system in time. From that system the generator of time evolution is read off and a Hilbert space is given where it generates a strongly continuous group. As a consequence the governing equation has a well-posed initial value problem. The spectrum of the generator relevant for stability considerations is shown to be equal to the spectrum of an operator polynomial whose coefficients can be read off from the governing equation. Finally, we give for the first time sufficient criteria for stability in the form of inequalities for the coefficients of the polynomial. These show that a negative canonical energy of the star does not necessarily indicate instability. It is still unclear whether these criteria are strong enough to prove stability for realistic stars.
2000
Article
http://edoc.mpg.de/3215
Proceedings of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences, v.458, 359-380 (2000)
en
oai:edoc.mpg.de:32252009-03-166:82
Black Holes
Brügmann, Bernd
Ghez, A. M.
Greiner, J.
2001
Conference-Paper
http://edoc.mpg.de/3225
PNAS, 19, 10525-10526 (2001)
Proceedings of Sixth Annual German-American Frontiers of Science Symposium, 10525-10526 (2001)
en
oai:edoc.mpg.de:32272009-03-166:82
Nonlinear and Perturbative Evolution of Distorted Black Holes: 2. Odd-parity Modes
Baker, John
Brandt, Steven
Campanelli, Manuela
Lousto, Carlos O.
Seidel, Edward
Takahashi, Ryoji
We study fully nonlinear and perturbative evolutions of nonrotating black holes with odd-parity distortions. Perturbative methods proved to be useful in order to interpret the nonlinear results. In particular, they provided insight on the nonlinear dependence of the wave forms with the distortion parameter Q(o) explaining it in terms of the multipole coupling. We also found an increase in the frequency of the wave forms in the nonlinear regime which results from the loss of a noticeable part of the initial total mass of the system to gravitational radiation producing effectively a drifting of the quasinormal frequencies. The nonlinear evolutions have been performed land cross checked) with the 3D parallel code for numerical relativity, CACTUs, and an independent axisymmetric code MAGOR. The linearized ones using the Regge-Wheeler formalism.
2000
Article
http://edoc.mpg.de/3227
Physical Review D, v.62 (2000)
en
oai:edoc.mpg.de:32452009-03-166:82
A data-analysis strategy for detecting gravitational-wave signals from inspiraling compact binaries with a network of laser-interferometric detectors
Pai, Archana
Dhurandhar, Sanjeev
Bose, Sukanta
A data-analysis strategy based on the maximum-likelihood method (MLM) is presented for the detection of gravitational waves from inspiraling compact binaries with a network of laser-interferometric detectors having arbitrary orientations and arbitrary locations around the globe. For simplicity, we restrict ourselves to the Newtonian inspiral wave form. However, the formalism we develop here is also applicable to a wave form with post-Newtonian (PN) corrections. The Newtonian wave form depends on eight parameters: the distance r to the binary, the phase delta (c) of the wave form at the time of final coalescence, the polarization-ellipse angle psi, the angle of inclination epsilon of the binary orbit to the line of sight, the source-direction angles {theta, phi}, the time of final coalescence t(c) at the fiducial detector, and the chirp time. All these parameters are relevant for a chirp search with multiple detectors, unlike the case of a single detector. The primary construct on which the MLM is based is the network likelihood ratio (LR). We obtain this ratio here. For the Newtonian inspiral wave form, the LR is a function of the eight signal parameters. In the MLM-based detection strategy, the LR must be maximized over all of these parameters. Here, we show that it is possible to maximize it analytically with respect to four of the eight parameters, namely, {r, delta (c), psi, epsilon}. Maximization over the time of arrival is handled most efficiently by using the fast-Fourier-transform algorithm, as in the case of a single detector. This not only allows us to scan the parameter space continuously over these five parameters but also cuts down substantially on the computational costs. The analytical maximization over the four parameters yields the optimal statistic on which the decision must be based. The value of the statistic also depends on the nature of the noises in the detectors. Here, we model these noises to be mainly Gaussian, stationary, and uncorrelated for every pair of detectors. Instances of non-Gaussianity, as are present in detector outputs, can be accommodated in our formalism by implementing vetoing techniques similar to those applied for single detectors. Our formalism not only allows us to express the likelihood ratio for the network in a very simple and compact form. but also is at the basis of giving an elegant geometric interpretation to the detection problem. Maximization of the LR over the remaining three parameters is handled as follows. Owing to the arbitrary locations of the detectors in a network, the time of arrival of a signal at any detector will, in general, be different from those at the others and, consequently, will result in signal time delays. For a given network, these time delays are determined by the source-direction angles {theta0, phi}, Therefore, to maximize the LR over the parameters {theta, phi} one needs to scan over the possible time delays allowed by a network. We opt for obtaining a bank of templates for the chirp time and the time delays. This means that we construct a bank of templates over xi, theta, and phi. We first discuss "idealized" networks with all the detectors having a common noise curve for simplicity. Such an exercise nevertheless yields useful estimates about computational costs, and also tests the formalism developed here. We then consider realistic cases of networks comprising the LIGO and VIRGO detectors: These include two-detector networks, which pair up the two LIGOs or VIRGO with one of the LIGOs, and the three-detector network that includes VIRGO and both the LIGOs.
2001
Article
http://edoc.mpg.de/3245
Physical Review D, v.64 (2001)
en
oai:edoc.mpg.de:33172009-03-166:82
Towards the solution of the relativistic gravitational radiation reaction problem for binary black holes
Lousto, Carlos O.
Here we present the results of applying the generalized Riemann zeta -function regularization method to the gravitational radiation reaction problem. We analyse in detail the head-on collision of two non-spinning black holes with an extreme mass ratio. The resulting reaction force on the smaller hole is repulsive. We discuss the possible extensions of these method to generic orbits and spinning black holes. The determination of corrected trajectories allows us to add second perturbative corrections with the consequent increase in the accuracy of computed waveforms.
2001
Conference-Paper
http://edoc.mpg.de/3317
Classical and Quantum Gravity, v.18, 19 (2001)
en
oai:edoc.mpg.de:33182009-03-166:82
Perturbations of the Kerr spacetime in horizon penetrating coordinates
Campanelli, Manuela
Laguna, Pablo
Pillin, Jorge
Ryan, Michael P.
Khanna, Gaurav
We derive the Teukolsky equation for perturbations of a Kerr spacetime when the spacetime metric is written in either ingoing or outgoing Kerr-Schild form. We also write explicit formulae for setting up the initial data for the Teukolsky equation in the time domain in terms of a 3-metric and an extrinsic curvature, The motivation of this work is to have in place a formalism to study the evolution in the 'close limit' of two recently proposed solutions to the initial-value problem in general relativity that are based on Kerr-Schild slicings. A perturbative formalism in horizon-penetrating coordinates is also very desirable in connection with numerical relativity simulations using black hole 'excision'.
2001
Article
http://edoc.mpg.de/3318
Classical and Quantum Gravity, v.18, 1543-1554 (2001)
en
oai:edoc.mpg.de:33192009-03-166:82
Gravitational field and equations of motion of spinning compact binaries to 2.5 post-Newtonian order
Tagoshi, Hideyuki
Ohashi, Akira
Owen, Benjamin J.
We derive spin-orbit coupling effects on the gravitational field and equations of motion of compact binaries in the 2.5 post-Newtonian approximation to general relativity, one PN order beyond when spin effects first appear. Our method iu based on that of Blanchet, Faye, and Ponsot, who use a past-Newtonian metric valid for general (continuous) fluids and represent pointlike compact objects with a delta -function stress-energy tensor, regularizing divergent terms by taking the Hadamard finite part. To obtain post-Newtonian spin effects, we use a different delta -function stress-energy tensor introduced by Bailey and Israel. In a future paper we will use the 2.5PN equations of motion For spinning bodies to derive the gravitational-wave luminosity and phase evolution of binary inspirals, which will be useful in constructing matched filters for signal analysis. The gravitational field derived here may help in posing initial data for numerical evolutions of binary black hole mergers.
2001
Article
http://edoc.mpg.de/3319
Physical Review D, v.63 (2001)
en
oai:edoc.mpg.de:33352009-03-166:82
Space Based Interferometric Detectors
Sintes, Alicia M.
World Scientific
2002
Conference-Paper
http://edoc.mpg.de/3335
Bishop, N.T. ; Maharaj, S.D.: Proceedings of the 16th International Conference on General Relativity and Gravitation, World Scientific, 455-456 (2002)
en
oai:edoc.mpg.de:33362009-03-166:82
Detector and Data Developments within GEO 600
Sintes, Alicia M.
2002
Article
http://edoc.mpg.de/3336
Matters of Gravity, the Newsletter of the Topical Group on Gravitation of the Americal Physical Society, v.19, 9-10 (2002)
en
oai:edoc.mpg.de:33612009-03-166:82
Searching for continuous gravitational wave signals: the hierarchical Hough transform algorithm
Papa, Maria Alessandra
Schutz, Bernard F.
Sintes, Alicia M.
It is well known that matched filtering techniques cannot be applied for searching extensive parameter space volumes for continuous gravitational wave signals. This is the reason why alternative strategies are being pursued. Hierarchical strategies are best at investigating a large parameter space when there exist computational power constraints. Algorithms of this kind are being implemented by all the groups that are developing software for analyzing the data of the gravitational wave detectors that will come online in the next years. In this talk we will report about the hierarchical Hough transform method that the GEO 600 data analysis team at the Albert Einstein Institute is developing. The three step hierarchical algorithm has been described elsewhere. In this talk we will focus on some of the implementational aspects we are currently concerned with.
2001
Conference-Paper
http://edoc.mpg.de/3361
Proceedings of the Conference "Gravitational waves: a challenge to theoretical astrophysics", 431-441 (2001)
en
oai:edoc.mpg.de:33652009-03-166:82
The close limit from a null point of view: The advanced solution
Campanelli, Manuela
Gomez, Roberto
Husa, Sascha
Winicour, Jeffrey
Zlochower, Yosef
We present a characteristic algorithm for computing the perturbation of a Schwarzschild spacetime by means of solving the Teukolsky equation. We implement the algorithm as a characteristic evolution code and apply it to compute the advanced solution to a black hole collision in the close approximation. The code successfully tracks the initial burst and quasinormal decay of a black hole perturbation through 10 orders of magnitude and tracks the final power law decay through an additional 6 orders of magnitude. Determination of the advanced solution, in which ingoing radiation is absorbed by the black hole but no outgoing radiation is emitted, is the first stage of a two stage approach to determining the retarded solution, which provides the close approximation waveform with the physically appropriate boundary condition of no ingoing radiation.
2001
Article
http://edoc.mpg.de/3365
Physical Review D, v.63 (2001)
en
oai:edoc.mpg.de:34022009-03-166:82
The Crustal Rigidity of a Neutron Star, and Implications for PSR 1828-11 and other Precession Candidates
Cutler, Curt
Ushomirsky, Greg
Link, Bennett
We calculate the crustal rigidity parameter, b, of a neutron star (NS), and show that b is a factor 40 smaller than the standard estimate due to Baym & Pines (1971). For a NS with a relaxed crust, the NS's free-precession frequency is directly proportional to b. We apply our result for b to PSR 1828-11, a 2.5 Hz pulsar that appears to be precessing with period 511 d. Assuming this 511-d period is set by crustal rigidity, we show that this NS's crust is not relaxed, and that its reference spin (roughly, the spin for which the crust is most relaxed) is 40 Hz, and that the average spindown strain in the crust is 5 imes 10^{-5}. We also briefly describe the implications of our b calculation for other well-known precession candidat
2003
Article
http://edoc.mpg.de/3402
Astrophysical Journal, v.588, 975-991 (2003)
en
oai:edoc.mpg.de:34032009-03-166:82
LISA, binary stars, and the mass of the gravitation
Cutler, Curt
Hiscock, William A.
Larson, Shane L.
We extend and improve earlier estimates of the ability of the proposed LISA (Laser Interferometer Space Antenna) gravitational wave detector to place upper bounds on the graviton mass, m_g, by comparing the arrival times of gravitational and electromagnetic signals from binary star systems. We show that the best possible limit on m_g obtainable this way is ~ 50 times better than the current limit set by Solar System measurements. Among currently known, well-understood binaries, 4U1820-30 is the best for this purpose; LISA observations of 4U1820-30 should yield a limit ~ 3-4 times better than the present Solar System bound. AM CVn-type binaries offer the prospect of improving the limit by a factor of 10, if such systems can be better understood by the time of the LISA mission. We briefly discuss the likelihood that radio and optical searches during the next decade will yield binaries that more closely approach the best possible case
2003
Article
http://edoc.mpg.de/3403
Physical Review D, v.67 (2003)
en
oai:edoc.mpg.de:34042009-03-166:82
Gravitational Waves from Neutron Stars with Large Toroidal B-fields
Cutler, Curt
We show that NS's with large toroidal B-fields tend naturally to evolve into potent gravitational-wave (gw) emitters. The toroidal field B_t tends to distort the NS into a prolate shape, and this magnetic distortion can easily dominate over the oblateness ''''frozen into'' the NS crust. An elastic NS with frozen-in B-field of this magnitude is clearly secularly unstable: the wobble angle between the NS's angular momentum J^i and the star's magnetic axis n_B^i grow on a dissipation timescale until J^i and n_B^i are orthogonal. This final orientation is clearly the optimal one for gravitational-wave (gw) emission. The basic cause of the instability is quite general, so we conjecture that the same final state is reached for a realistic NS. Assuming this, we show that for LMXB's with B_t of order 10^{13}G, the spindown from gw's is sufficient to balance the accretion torque--supporting a suggestion by Bildsten. The spindown rates of most millisecond pulsars can also be attributed to gw emission sourced by toroidal B-fields, and both these sources could be observed by LIGO II. While the first-year spindown of a newborn NS is most likely dominated by em processes, reasonable values of B_t and the (external) dipolar field B_d can lead to detectable levels of gw emission, for a newborn NS in our own galaxy
2002
Article
http://edoc.mpg.de/3404
Physical Review D, v.66 (2002)
oai:edoc.mpg.de:34052009-03-166:82
An Overview of Gravitational-Wave Sources
Cutler, Curt
Thorne, Kip S.
We review current best estimates of the strength and detectability of the gravitational waves from a variety of sources, for both ground-based and space-based detectors, and we describe the information carried by the waves.
World Scientific
2002
Conference-Paper
http://edoc.mpg.de/3405
Bishop, Nigel T.; Maharaj, S.: General Relativity and Gravitation : Proceedings of the 16th International Conference on General Relativity and Gravitation, World Scientific, 72-112 (2002)
en
oai:edoc.mpg.de:34862009-03-166:82
Evolutions of Stellar Oscillations
Allen, Gabrielle
Andersson, Nils
Kokkotas, Kostas D.
Schutz, Bernard F.
World Scientific
1999
Conference-Paper
http://edoc.mpg.de/3486
Piran, T.: Proceedings of 8th Marcel Grossmann Meeting on General Relativity, World Scientific, 732-734 (1999)
en
oai:edoc.mpg.de:34882009-03-166:82
Gravitational Waves and Neutron Stars
Schutz, Bernard F.
Astronomical Society of the Pacific 202
2001
Conference-Paper
http://edoc.mpg.de/3488
Kramer, M.; Wex, N.; Wielebinski, R: Proceedings of Pulsar Astronomy-2000 and beyond, IAU Colloquium 177, Astronomical Society of the Pacific 202, 727-732 (2001)
en
oai:edoc.mpg.de:34982009-03-166:82
Gravitational Waves, Sources and Detectors
Schutz, Bernard F.
Ricci, Franco
Gravitational waves and their detection are becoming more and more important both for the theoretical physicist and the astrophysicist. In fact, technological developments have enabled the construction such sensitive detectors (bars and interferometers) that the detection of gravitational radiation could become a reality during the next few years. In these lectures we give a brief overview of this interesting and challenging field of modern physics. The topics to be covered are divided into 6 lectures: elements of gravitational waves, gravitational wave detectors, sources, energy, mass- and current-quadrupole radiation, and examples of source calculations
Institute of Physics
2001
InBook
http://edoc.mpg.de/3498
Gravitational Waves, 11-83 (2001)
en
oai:edoc.mpg.de:35252009-03-166:82
Galacitic Collapse of Scalar Field Dark Matter
Alcubierre, Miguel
Guzman, F. Siddhartha
Matos, Tonatiuh
Nunez, Dario
Urena-Lopez, L. Arturo
Wiederhold, Petra
We present a scenario for galaxy formation based on the hypothesis of scalar field dark matter. We interpret galaxy formation through the collapse of a scalar field fluctuation. We find that a cosh potential for the self-interaction of the scalar field provides a reasonable scenario for galactic formation, which is in agreement with cosmological observations and phenomenological studies in galaxies.
2002
Article
http://edoc.mpg.de/3525
Classical and Quantum Gravity, v.19, 5017-5024 (2002)
en
oai:edoc.mpg.de:35272009-04-066:82
The Scope of a Functional Calculus Approach to Fractional Differential Equations
Kempfle, Siegmar
Beyer, Horst
This paper presents a functional calculus definition of linear fractional (pseudo)differential operators via generalised Fourier transforms as a natural extension of integer ordered derivatives. First, we describe the extension of our L-2-based functional calculus approach on D'. Second, we demonstrate that important computational rules as well as properties of integer ordered differential operators are preserved by our approach. This concerns also the D'-kernel of our operators which belong to the same class as those corresponding to integer derivatives, i.e., they are linear combinations of "polynomials times exponential functions".
2003
Conference-Paper
http://edoc.mpg.de/3527
Begehr, H.G.W; Gilbert, R.P; Wong, M.W: PROGRESS IN ANALYSIS, VOLS I AND II, 69-81 (2003)
en
oai:edoc.mpg.de:35322009-03-166:82
Testing the Cactus code on exact solutions of Einstein field equations
Vulcanov, Dumitru N.
Alcubierre, Miguel
The article presents a series of numerical simulations of exact solutions of the Einstein equations performed using the Cactus code, a complete 3-dimensional machinery for numerical relativity. We describe an application (''''thorn'') for the Cactus code that can be used for evolving a variety of exact solutions, with and without matter, including solutions used in modern cosmology for modeling the early stages of the universe. Our main purpose has been to test the Cactus code on these well-known examples, focusing mainly on the stability and convergence of the code
2002
Article
http://edoc.mpg.de/3532
International Journal of Modern Physics C, v.13, 805-821 (2002)
en
oai:edoc.mpg.de:35332009-04-216:82
Remarks on a solvable cosmological model
Cotaescu, Ion I.
Vulcanov, Dumitru N.
We present an exact analytical solution of the Einstein equations with cosmological constant in a spatially flat Robertson-Walker metric. This is interpreted as an isotropic Lemaitre-type version of the cosmological Friedmann model. Implications in the recent discovered cosmic acceleration of the universe and in the theory of an inflationary model of the universe are in view. Some properties of this solution are pointed out as a result of numerical investigations of the model.
2003
Article
http://edoc.mpg.de/3533
Europhysics Letters (2003)
en
oai:edoc.mpg.de:35342009-03-166:82
Lighthouses of Gravitational Wave Astronomy
Schutz, Bernard F.
Gravitational wave detectors capable of making astronomical observations could begin to operate within the next year, and over the next 10 years they will extend their reach out to cosmological distances, culminating in the space mission LISA. A prime target of these observatories will be binary systems, especially those whose orbits shrink measurably during an observation period. These systems are standard candles, and they offer independent ways of measuring cosmological parameters. LISA in particular could identify the epoch at which star formation began and, working with telescopes making electromagnetic observations, measure the Hubble flow at redshifts out to 4 or more with unprecedented accuracy
Springer
2002
Conference-Paper
http://edoc.mpg.de/3534
Gilfanov, M.: Lighthouses of the universe : the most luminous celestical objects and their use for cosmology ; proceedings of the MPA ESO MPE USM Joint Astronomy Conference, Springer, 207-224 (2002)
en
oai:edoc.mpg.de:35352009-03-166:82
Vortex Unpinning in Precessing Neutron Stars
Link, Bennett
Cutler, Curt
The neutron vortices thought to exist in the inner crust of a neutron star interact with nuclei and are expected to pin to the nuclear lattice. Evidence for long-period precession in pulsars, however, requires that pinning be negligible. We estimate the strength of vortex pinning and show that hydrodynamic forces present in a precessing star are likely sufficient to unpin all of the vortices of the inner crust. In the absence of precession, however, vortices could pin to the lattice with sufficient strength to explain the giant glitches observed in many radio pulsars
2002
Article
http://edoc.mpg.de/3535
Monthly Notices of the Royal Astronomical Society, v.336, 211-216 (2002)
en
oai:edoc.mpg.de:214782009-03-166:82
A Fast Apparent-Horizon Finder for 3-Dimensional Cartesian Grids in Numerical Relativity
Thornburg, Jonathan
In 3+1 numerical simulations of dynamic black hole spacetimes, it's useful to be able to find the apparent horizon(s) (AH) in each slice of a time evolution. A number of AH finders are available, but they often take many minutes to run, so they're too slow to be practically usable at each time step. Here I present a new AH finder,_AHFinderDirect_, which is very fast and accurate, typically taking only a few seconds to find an AH to $\sim 10^{-5} m$ accuracy on a GHz-class processor. I assume that an AH to be searched for is a Strahlk\"orper (star-shaped region) with respect to some local origin, and so parameterize the AH shape by $r = h(angle)$ for some single-valued function $h: S^2 \to \Re^+$. The AH equation then becomes a nonlinear elliptic PDE in $h$ on $S^2$, whose coefficients are algebraic functions of $g_{ij}$, $K_{ij}$, and the Cartesian-coordinate spatial derivatives of $g_{ij}$. I discretize $S^2$ using 6 angular patches (one each in the neighborhood of the $\pm x$, $\pm y$, and $\pm z$ axes) to avoid coordinate singularities, and finite difference the AH equation in the angular coordinates using 4th order finite differencing. I solve the resulting system of nonlinear algebraic equations (for $h$ at the angular grid points) by Newton's method, using a "symbolic differentiation" technique to compute the Jacobian matrix._AHFinderDirect_ is implemented as a thorn in the_Cactus_ computational toolkit, and will be made freely available starting in summer 2003
2004
Article
http://edoc.mpg.de/21478
Classical and Quantum Gravity, v.21, 743-766 (2004)
en
oai:edoc.mpg.de:236952009-03-166:82
Median based line tracker (MBLT): model independent and transient preserving line removal from interferometric data
Mohanty, Soumya
2002
Article
http://edoc.mpg.de/23695
Classical Quantum Gravity, v.19, 1513-1519 (2002)
en
oai:edoc.mpg.de:237282009-03-166:82
Templates for stellar mass black holes falling into supermassive black holes
Sathyaprakash, B. S.
Schutz, Bernard F.
The spin-modulated gravitational wave signals, which we shall call smirches, emitted by stellar mass black holes, tumbling and inspiralling into massive black holes, have extremely complicated shapes. Tracking these signals with the aid of pattern matching techniques, such as Wiener filtering, is likely to be computationally an impossible exercise. In this paper we propose using a mixture of optimal and non-optimal methods to create a search hierarchy to ease the computational burden. Furthermore, by employing the method of principal components (also known as singular value decomposition) we explicitly demonstrate that the effective dimensionality of the search parameter space of smirches is likely to be just 3 or 4, much smaller than what has hitherto been thought to be about 9 or 10. This result, based on a limited study of the parameter space, should be confirmed by a more exhaustive study over the parameter space as well as Monte Carlo simulations to test the predictions made in this paper.
2003
Article
http://edoc.mpg.de/23728
Classical and Quantum Gravity, v.20, S209-S218 (2003)
en
oai:edoc.mpg.de:237442009-03-176:82
Gauge conditions for long-term numerical black hole evolutions with or without excision
Alcubierre, Miguel
Brügmann, Bernd
Pollney, Denis
Seidel, Edward
Takahashi, Ryoji
Springer
2003
Conference-Paper
http://edoc.mpg.de/23744
Fernández-Jambrina, Leonardo; González-Romero, Luis Manuel: Current Trends in Relativistic Astrophysics: Theoretical, Numerical, Observational, Springer, 140-158 (2003)
oai:edoc.mpg.de:509502009-03-166:82
Nonlinear multidimensional cosmological models with form fields: stabilization of extra dimensions and the cosmological constant problem
Günther, U.
Moniz, P.
Zhuk, A.
We consider multidimensional gravitational models with a nonlinear scalar curvature term and form fields in the action functional. In our scenario it is assumed that the higher dimensional spacetime undergoes a spontaneous compactification to a warped product manifold. Particular attention is paid to models with quadratic scalar curvature terms and a Freund-Rubin-like ansatz for solitonic form fields. It is shown that for certain parameter ranges the extra dimensions are stabilized. In particular, stabilization is possible for any sign of the internal space curvature, the bulk cosmological constant and of the effective four-dimensional cosmological constant. Moreover, the effective cosmological constant can satisfy the observable limit on the dark energy density. Finally, we discuss the restrictions on the parameters of the considered nonlinear models and how they follow from the connection between the D–dimensional and the four-dimensional fundamental mass scales.
2003
Article
http://edoc.mpg.de/50950
Physical Review D, v.68 (2003)
en
oai:edoc.mpg.de:509662009-04-216:82
Search for Periodic Gravitational Wave Sources with the EXPLORER detector
Astone, P.
Bassan, M.
Bonifazi, P.
Carelli, P.
Coccia, E.
Cosmelli, C.
D'Antonio, S.
Fafone, V.
Frasca, Sergio
Minenkov, Y.
Modena, I.
Modestino, G.
Moleti, A.
Pallottino, G. V.
Papa, Maria Alessandra
Pizzella, G.
Quintieri, L.
Terenzi, R.
Visco, M.
We have developed a procedure for the search of signals from periodic sources in the data of gravitational wave detectors. We report here the analysis of one year of data from the resonant detector Explorer, searching for sources located in the Galactic Center (GC). No signals with amplitude greater than h-bar = 2.9×10–24, in the range 921.32–921.38 Hz, were observed using data collected over a time period of 95.7 days, for a source located at alpha= 17.70±0.01 h and delta= –29.00±0.05 deg. Our procedure can be extended for any assumed position in the sky and for a more general all-sky search, with the proper frequency correction to account for the spin-down and Doppler effects.
2002
Article
http://edoc.mpg.de/50966
Physical Review D 65, v.65 (2002)
en
oai:edoc.mpg.de:509712009-03-166:82
Numerical studies of Phi2-Oscillatons
Alcubierre, Miguel
Becerril, Ricardo
Guzman, F. Siddhartha
Matos, Tonatiuh
Nunez, Dario
Urena-Lopez, L. Arturo
2003
Article
http://edoc.mpg.de/50971
Classical and Quantum Gravity, v.20, 2883-2903 (2003)
oai:edoc.mpg.de:509822009-04-066:82
Contribution to the EAC Meeting Report by the LIGO-GriPhyN Working Group
Bharati, Amit Agarwal Shishir
Blythe, James
Deelman, Ewa
Gil, Yolanda
Kesselman, Carl
Mehta, Gaurang
Patil, Sonal
Rao, Srividya
Singh, Gurmeet
Thiebaux, Marcus
Vahi, Karan
Anderson, Stuart
Papa, Maria Alessandra
Sintes, Alicia M.
LIGO REPORT: LIGO-T030005-00-E 2003-01-09, 2003
2003
Interactive Resource
http://edoc.mpg.de/50982
en
oai:edoc.mpg.de:510042009-03-166:82
Newtonian Collapse of Scalar Field Dark Matter
Guzman, F. Siddhartha
Urena-Lopez, L. Arturo
In this letter, we develop a Newtonian approach to the collapse of galaxy fluctuations of scalar field dark matter under initial conditions inferred from simple assumptions. The full relativistic system, the so called Einstein-Klein-Gordon, is reduced to the Schr¨odinger-Newton one in the weak field limit. The scaling symmetries of the SN equations are exploited to track the non-linear collapse of single scalar matter fluctuations. The results can be applied to both real and complex scalar fields.
2003
Article
http://edoc.mpg.de/51004
Physical Review D, v.68 (2003)
en
oai:edoc.mpg.de:510352009-03-166:82
Toward standard testbeds for numerical relativity
Alcubierre, Miguel
Allen, Gabrielle
Bona, Carles
Fiske, David R.
Goodale, Tom
Guzman, F. Siddhartha
Hawke, Ian
Hawley, Scott H.
Husa, Sascha
Koppitz, Michael
Lechner, Christiane
Pollney, Denis
Rideout, David
Salgado, Marcelo
Schnetter, Erik
Seidel, Edward
Shinkai, Hisa-aki
Shoemaker, Deirdre
Szilagyi, Bela
Takahashi, Ryoji
Winicour, Jeffrey
In recent years, many different numerical evolution schemes for Einstein's equations have been proposed to address stability and accuracy problems that have plagued the numerical relativity community for decades. Some of these approaches have been tested on different spacetimes, and conclusions have been drawn based on these tests. However, differences in results originate from many sources, including not only formulations of the equations, but also gauges, boundary conditions, numerical methods and so on. We propose to build up a suite of standardized testbeds for comparing approaches to the numerical evolution of Einstein's equations that are designed to both probe their strengths and weaknesses and to separate out different effects, and their causes, seen in the results. We discuss general design principles of suitable testbeds, and we present an initial round of simple tests with periodic boundary conditions. This is a pivotal first step towards building a suite of testbeds to serve the numerical relativists and researchers from related fields who wish to assess the capabilities of numerical relativity codes. We present some examples of how these tests can be quite effective in revealing various limitations of different approaches, and illustrating their differences. The tests are presently limited to vacuum spacetimes, can be run on modest computational resources and can be used with many different approaches used in the relativity community.
2004
Article
http://edoc.mpg.de/51035
Classical and Quantum Gravity, v.21, 589-613 (2004)
en
oai:edoc.mpg.de:510392009-03-166:82
A new general purpose event horizon finder for 3D numerical spacetimes
Diener, Peter
I present a new general purpose event horizon finder for full 3D numerical spacetimes. It works by evolving a complete null surface backwards in time. The null surface is described as the zero level set of a scalar function, that in principle is defined everywhere. This description of the surface allows the surface, trivially, to change topology, making this event horizon finder able to handle numerical spacetimes, where two (or more) black holes merge into a single final black hole.
2003
Article
http://edoc.mpg.de/51039
Classical and Quantum Gravity, v.20, 4901-4918 (2003)
en
oai:edoc.mpg.de:510512009-03-166:82
Maximal Slicing for Puncture Evolutions of Schwarzschild and Reissner-Nordström Black Holes
Reimann, Bernd
Bruegmann, Bernd
We prove by explicit construction that there exists a maximal slicing of the Schwarzschild spacetime such that the lapse has zero gradient at the puncture. This boundary condition has been observed to hold in numerical evolutions, but in the past it was not clear whether the numerically obtained maximal slices exist analytically. We show that our analytical result agrees with numerical simulation. Given the analytical form for the lapse, we can derive that at late times the value of the lapse at the event horizon approaches the value ${3/16}\sqrt{3} \approx 0.3248$, justifying the numerical estimate of 0.3 that has been used for black hole excision in numerical simulations. We present our results for the non-extremal Reissner-Nordström metric, generalizing previous constructions of maximal slices.
2004
Article
http://edoc.mpg.de/51051
Physical Review D, v.69 (2004)
en
oai:edoc.mpg.de:510892009-04-216:82
Swift Pointing and Gravitational-Wave Bursts from Gamma-Ray Burst Events
Finn, Lee Samuel
Krishnan, Badri
Sutton, Patrick J.
The currently accepted model for gamma-ray burst phenomena involves the violent formation of a rapidly rotating solar-mass black hole. Gravitational waves should be associated with the black-hole formation, and their detection would permit this model to be tested. Even upper limits on the gravitational-wave strength associated with gamma-ray bursts could constrain the gamma-ray burst model. This requires joint observations of gamma-ray burst events with gravitational and gamma-ray detectors. Here we examine how the quality of an upper limit on the gravitational-wave strength associated with gamma-ray bursts depends on the relative orientation of the gamma-ray-burst and gravitational-wave detectors, and apply our results to the particular case of the Swift Burst-Alert Telescope (BAT) and the LIGO gravitational-wave detectors. A result of this investigation is a science-based ``figure of merit'' that can be used, together with other mission constraints, to optimize the pointing of the Swift telescope for the detection of gravitational waves associated with gamma-ray bursts.
2003
Article
http://edoc.mpg.de/51089
Classical and Quantum Gravity, v.20, 815-820 (2003)
en
oai:edoc.mpg.de:511662009-04-216:82
Swift Pointing and the Association Between Gamma-Ray Bursts and Gravitational-Wave Bursts
Finn, Lee Samuel
Krishnan, Badri
Sutton, Patrick J.
The currently accepted model for gamma-ray burst phenomena involves the violent formation of a rapidly rotating solar mass black hole. Gravitational waves should be associated with the black-hole formation, and their detection would permit this model to be tested, the black hole progenitor (e.g., coalescing binary or collapsing stellar core) identified, and the origin of the gamma rays (within the expanding relativistic fireball or at the point of impact on the interstellar medium) located. Even upper limits on the gravitational-wave strength associated with gamma-ray bursts could constrain the gamma-ray burst model. To do any of these requires joint observations of gamma-ray burst events with gravitational and gamma-ray detectors. Here we examine how the quality of an upper limit on the gravitational-wave strength associated with gamma-ray burst observations depends on the relative orientation of the gamma-ray-burst and gravitational-wave detectors, and apply our results to the particular case of the Swift Burst-Alert Telescope (BAT) and the LIGO gravitational-wave detectors. A result of this investigation is a science-based ``figure of merit'' that can be used, together with other mission constraints, to optimize the pointing of the Swift telescope for the detection of gravitational waves associated with gamma-ray bursts.
2004
Article
http://edoc.mpg.de/51166
Astrophysical Journal, v.607, 384-390 (2004)
en
oai:edoc.mpg.de:511672009-04-216:82
Black Hole Spectroscopy: Testing General Relativity through Gravitational Wave Observations
Dreyer, Olaf
Kelly, Bernard J.
Krishnan, Badri
Finn, Lee Samuel
Garrison, David
Lopez-Aleman, Ramon
Assuming that general relativity is the correct theory of gravity in the strong field limit, can gravitational wave observations distinguish between black hole and other compact object sources? Alternatively, can gravitational wave observations provide a test of one of the fundamental predictions of general relativity? Here we describe a definitive test of the hypothesis that observations of damped, sinusoidal gravitational waves originated from a black hole or, alternatively, that nature respects the general relativistic no-hair theorem. For astrophysical black holes, which have a negligible charge-to-mass ratio, the black hole quasi-normal mode spectrum is characterized entirely by the black hole mass and angular momentum and is unique to black holes. In a different theory of gravity, or if the observed radiation arises from a different source (e.g., a neutron star, strange matter or boson star), the spectrum will be inconsistent with that predicted for general relativistic black holes. We give a statistical characterization of the consistency between the noisy observation and the theoretical predictions of general relativity, together with a numerical example.
2004
Article
http://edoc.mpg.de/51167
Classical and Quantum Gravity, v.21, 787-804 (2004)
en
oai:edoc.mpg.de:511732009-03-166:82
Quantum Gravity and the Big Bang
Bojowald, Martin
Quantum gravity has matured over the last decade to a theory which can tell in a precise and explicit way how cosmological singularities of general relativity are removed. A branch of the universe "before" the classical big bang is obtained which is connected to ours by quantum evolution through a region around the singularity where the classical space-time dissolves. We discuss the basic mechanism as well as applications ranging to new phenomenological scenarios of the early universe expansion, such as an inflationary period.
Institut Universitaire de Formation des Maîtres (IUFM)
2004
Conference-Paper
http://edoc.mpg.de/51173
en
oai:edoc.mpg.de:596452009-03-166:82
Equation of motion for relativistic compact binaries with the strong field point particle limit: Third post-Newtonian order
Itoh, Yousuke
An equation of motion for relativistic compact binaries is derived through the third post-Newtonian (3 PN) approximation of general relativity. The strong field point particle limit and multipole expansion of the stars are used to solve iteratively the harmonically relaxed Einstein equations. We take into account the Lorentz contraction on the multipole moments defined in our previous works. We then derive a 3 PN acceleration of the binary orbital motion of the two spherical compact stars based on a surface integral approach which is a direct consequence of local energy momentum conservation. Our resulting equation of motion admits a conserved energy (neglecting the 2.5 PN radiation reaction effect), is Lorentz invariant and is unambiguous: there exist no undetermined parameter reported in the previous works. We shall show that our 3 PN equation of motion agrees physically with the Blanchet and Faye 3 PN equation of motion if $\lambda = - 1987/3080$, where $\lambda$ is the parameter which is undetermined within their framework. This value of $\lambda$ is consistent with the result of Damour, Jaranowski, and Schäfer who first completed a 3 PN iteration of the ADM Hamiltonian in the ADMTT gauge using the dimensional regularization.
2004
Article
http://edoc.mpg.de/59645
Physical Review D, v.69 (2004)
en
oai:edoc.mpg.de:597212009-03-166:82
New derivation of a third post-Newtonian equation of motion for relativistic compact binaries without ambiguity
Itoh, Yousuke
Futamase, Toshifumi
A third post-Newtonian (3 PN) equation of motion for an inspiralling binary consisting of two spherical compact stars with strong internal gravity is derived under harmonic coordinate condition using the strong field point particle limit. The equation of motion is complete in a sense that it is Lorentz invariant in the post-Newtonian perturbative sense, admits conserved energy of the orbital motion, and is unambiguous, that is, with no undetermined coefficient. In this paper, we show explicit expressions of the 3 PN equation of motion and an energy of the binary orbital motion in case of the circular orbit (neglecting the 2.5 PN radiation reaction effect) and in the center of the mass frame. It is argued that the 3 PN equation of motion we obtained is physically unambiguous. Full details will be reported elsewhere.
2003
Article
http://edoc.mpg.de/59721
Physical Review D, v.68 (2003)
en
oai:edoc.mpg.de:597222009-03-166:82
Black hole initial data from a non-conformal decomposition
Bishop, Nigel T.
Beyer, Florian
Koppitz, Michael
We present an alternative approach to setting initial data in general relativity. We do not use a conformal decomposition, but instead express the 3-metric in terms of a given unit vector field and one unknown scalar field. In the case of axisymmetry, we have written a program to solve the resulting nonlinear elliptic equation. We have obtained solutions, both numerically and from a linearized analytic method, for a general perturbation of Schwarzschild.
2004
Article
http://edoc.mpg.de/59722
Physical Review D, v.69 (2004)
en
oai:edoc.mpg.de:601912009-03-166:82
Late Time Analysis for Maximal Slicing of Reissner-Nordström Puncture Evolutions
Reimann, Bernd
Bruegmann, Bernd
We perform an analytic late time analysis for maximal slicing of the Reissner-Nordstr\"om black hole spacetime. In particular, we discuss the collapse of the lapse in terms of its late time behavior at the throat and at the event horizon for the even and the puncture lapse. In the latter case we also determine the value of the lapse at the puncture. Furthermore, in the limit of late times slice stretching effects are studied as they arise for maximal slicing of puncture evolutions. We perform numerical experiments for a Schwarzschild black hole with puncture lapse and find agreement with the analytical results.
2004
Article
http://edoc.mpg.de/60191
Physical Review D, v.69 (2004)
en
oai:edoc.mpg.de:602062009-03-176:82
The phase-integral method and blank hole normal modes
Andersson, Nils
Araujo, M. E.
Schutz, Bernard F.
The phase-integral method has proved to be a powerful tool for studying the quasinormal modes of black holes. A generalization of the WKB methods of quantum mechanics, its treatment of the complex coordinate plane brings a number of important simplifications and potentially powerful computational aids to bear on the problem of computing eigenfrequencies with large imaginary parts. It holds great promise of further applications to related problems, such as the quasinormal modes of relativistic stars. However, in some respects the method is incomplete, particularly in its assessment of error bounds. The authors make available to researchers in the field of relativity a simple and self-contained introduction to the fundamental concepts of the phase-integral method, in which they also point out areas that seem to need further development. As an example of the use of the method, they derive the two-transition-point phase-integral formula for quasinormal modes of the Schwarzschild black hole, which is an accurate asymptotic approximation for the first modes. They provide the foundation for related papers in which they use the method to develop accurate asymptotic expressions for highly damped modes.
1993
Article
http://edoc.mpg.de/60206
Classical and Quantum Gravity, v.10, 735-755 (1993)
en
oai:edoc.mpg.de:602072009-03-176:82
Generalized Bohr-Sommerfeld formula for Schwarzschild black hole normal modes
Andersson, Nils
Araujo, M. E.
Schutz, Bernard F.
A generalized Bohr-Sommerfeld-type formula determining the quasinormal-mode frequencies of Schwarzschild black holes is derived using the phase-integral method with three transition points. The formula is valid provided that these points are well separated from each other, and is remarkably accurate for the high-overtone modes. It makes a great improvement over the conventional Bohr-Sommerfeld formula, derived from two transition points.
1993
Article
http://edoc.mpg.de/60207
Classical and Quantum Gravity, v.10, 757-765 (1993)
en
oai:edoc.mpg.de:602082009-03-176:82
On the Bohr-Sommerfeld formula for black hole normal modes
Araujo, M. E.
Nicholson, David
Schutz, Bernard F.
The authors present a derivation of the Bohr-Sommerfeld formula based by Guinn et al (1990) to successfully calculate the complex eigenfrequencies for the low-lying quasi-normal modes of a Schwarzschild black hole. It is shown that this formula is valid even when the transition points under consideration come close together.
1993
Article
http://edoc.mpg.de/60208
Classical and Quantum Gravity, v.10, 1127-1138 (1993)
en
oai:edoc.mpg.de:602092009-03-176:82
Robinson-Trautman Equations and Chandrasekhar's Special Perturbation of the Schwarzschild Metric
Qi, Guoying
Schutz, Bernard F.
1993
Article
http://edoc.mpg.de/60209
General Relativity and Gravitation, v.25, 1185-1188 (1993)
oai:edoc.mpg.de:602102009-03-176:82
Gravitational Waves and Numerical Relativity
Schutz, Bernard F.
Wiley Eastern
1993
Conference-Paper
http://edoc.mpg.de/60210
Iyer; B. R. [et al.]: Advances in gravitation and cosmology : proceedings of the Second International Conference on Gravitation and Cosmology, Wiley Eastern, 109-119 (1993)
en
oai:edoc.mpg.de:602112009-03-176:82
Sources of Gravitational Waves and their detectability
Schutz, Bernard F.
Institute of Physics Publ.
1993
Conference-Paper
http://edoc.mpg.de/60211
Gleiser, R.J.; Kozameh, C.N.; Moreschi, O.M.: General relativity and gravitation 1992 : proceedings of the thirteenth International Conference on General Relativity and Gravitation, Institute of Physics Publ., 191-209 (1993)
en
oai:edoc.mpg.de:602122009-03-176:82
Cosmic sources of gravitational radiation
Schutz, Bernard F.
The most likely sources of gravitational radiation that may be seen by the large-scale laser-interferometric detectors that will soon be built around the world are reviewed. The prospects for detection are excellent, and much information can be extracted. But the coalescences of compact objects pose a problem: the two-body problem in relativity is not well enough understood to allow one to extract the most information from a detection. There is a challenge to relativists to find solutions that will be useful to gravitational wave detectors.
1993
Article
http://edoc.mpg.de/60212
Classical and Quantum Gravity, v.10, S135-S145 (1993)
en
oai:edoc.mpg.de:602132009-03-176:82
Gravitation and General Relativity
Schutz, Bernard F.
Will, Clifford M.
Wiley - VCH
1993
InBook
http://edoc.mpg.de/60213
Encyclopedia of Applied Physics, 303-340 (1993)
en
oai:edoc.mpg.de:602142009-03-176:82
Time-Symmetric ADI and Causal Reconnection: Stable Numerical Techniques for Hyperbolic Systems on Moving Grids
Alcubierre, Miguel
Schutz, Bernard F.
Moving grids are of interest in the numerical solution of hydrodynamical problems and in numerical relativity. We show that conventional integration methods for the simple wave equation in one and more than one dimension exhibit a number of instabilities on moving grids. We introduce two techniques, which we call causal reconnection and time-symmetric ADI, which together allow integration of the wave equation with absolute local stability in any number of dimensions on grids that may move very much faster than the wave speed and that can even accelerate. These methods allow very long time-steps, are fully second-order accurate, and offer the computational efficiency of operator-splitting. We develop causal reconnection first in the one-dimensional case; we find that a conventional implicit integration scheme that is unconditionally stable as long as the speed of the grid is smaller than that of the waves nevertheless turns unstable whenever the grid speed increases beyond this value. We introduce a notion of local stability for difference equations with variable coefficients. We show that, by "reconnecting" the computational molecule at each time-step in such a way as to ensure that its members at different time-steps are within one another's causal domains, one eliminates the instability, even if the grid accelerates. This permits very long time-steps on rapidly moving grids. The method extends in a straightforward and efficient way to more than one dimension. However, in more than one dimension, it is very desirable to use operator-splitting techniques to reduce the computational demands of implicit methods, and we find that standard schemes for integrating the wave equation––Lees' first and second alternating direction implicit (ADI) methods––go unstable for quite small grid velocities. Lees' first method, which is only first-order accurate on a shifting grid, has mild but nevertheless significant instabilities. Lees' second method, which is second-order accurate, is very unstable. By adopting a systematic approach to the design of ADI schemes, we develop a new ADI method that cures the instability for all velocities in any direction up to the wave speed. This scheme is uniquely defined by a simple physical principle: the ADI difference equations should be invariant under time-inversion. (The wave equation itself and the fully implicit difference equations satisfy this criterion, but neither of Lees' methods do.) This new time-symmetric ADI scheme is, as a bonus, second-order accurate. It is thus far more efficient than a fully implicit scheme, just as stable, and just as accurate. By implementing causal reconnection of the computational molecules, we extend the time-symmetric ADI scheme to arrive at a scheme that is second-order accurate, computationally efficient, and unconditionally locally stable for all grid speeds and long time-steps. We have tested the method by integrating the wave equation on a rotating grid, where it remains stable even when the grid speed at the edge is 15 times the wave speed. Because our methods are based on simple physical principles, they should generalize in a straightforward way to many other hyperbolic systems. We discuss briefly their application to general relativity and their potential generalization to fluid dynamics.
1994
Article
http://edoc.mpg.de/60214
Journal of Computational Physics, v.112, 44-77 (1994)
en
oai:edoc.mpg.de:602152009-03-176:82
Quasinormal modes of Reissner-Nordström black holes: Phase-integral approach
Andersson, Nils
Araujo, M. E.
Schutz, Bernard F.
1994
Article
http://edoc.mpg.de/60215
Physical Review D, v.49, 2703-2709 (1994)
en
oai:edoc.mpg.de:602162009-03-176:82
Filtering coalescing binary signals: Issues concerning narrow banding, thresholds, and optimal sampling
Dhurandhar, Sanjeev
Schutz, Bernard F.
When the raw output of a gravitational wave detector is correlated with the matched filter of a coalescing binary wave form the filtered output shows a periodic behavior—it rings at a certain frequency. This phenomenon could be worrisome since the signal peak in the filtered output might be reduced if it falls in the ``trough'' of the sinusoid. In this paper we address this question and present a detailed examination of the ringing which is caused by the effective narrow banding by the matched filter of detector noise. We first solve the problem for an idealized ``box'' filter and show that the ringing frequency is roughly the central frequency of the box if the box is not too wide. For an idealized coalescing binary filter we show that the expected value of this frequency is 1.27 fs where fs is the seismic noise cutoff of the detector. The ringing implies that there is some redundancy in the filtered ouput. Also the autocorrelation function of the filtered output resembles the sinc function, and hence adjacent sample points are correlated, i.e., the filtered output is colored. These two phenomena are related and have a bearing on the setting up of thresholds and also suggest that we resample the filtered output at a coarser rate. We investigate the problem of thresholds when the filtered output is colored and obtain relations between the false alarm probabilities and threshold levels. Finally we suggest optimal sampling rates so that the resampled filtered output is uncorrelated.
1994
Article
http://edoc.mpg.de/60216
Physical Review D, v.50, 2390-2405 (1994)
en
oai:edoc.mpg.de:602172009-03-176:82
Gravitational waves
Schutz, Bernard F.
In the last few years there have been a number of significant developments in research towards the detection of gravitational radiation from astronomical objects. The construction of 3 large-scale (3- or 4-km) interferometric detectors has been funded; new high-sensitivity bars are under construction; there is a serious proposal using two interferometers has been used to put the data from the first coincidence observation using two interferometers has been used to put upper limits on gravitational wave bursts; and new theoretical studies of the relativistic two-body problem have shown that observations of the coalescences of two neutron stars or black holes from binary orbits can provide detailed information about the stars' masses and spins –– but only if we can solve the two-body problem better than we have done so far. These developments are reviewed here.
1994
Article
http://edoc.mpg.de/60217
Nuclear Physics B - Proceedings Supplements, v.35, 44-53 (1994)
en
oai:edoc.mpg.de:602182009-03-176:82
A new numerical approach to the oscillation modes of relativistic stars
Andersson, Nils
Kokkotas, Kostas D.
Schutz, Bernard F.
The oscillation modes of a simple polytropic stellar model are studied. Using a new numerical approach (based on integration for complex coordinates) to the problem for the stellar exterior we have computed the eigenfrequencies of the highly damped w modes. The results obtained agree well with recent ones of Leins, Nollert & Soffel. Specifically, we are able to explain why several modes in this regime of the complex frequency plane could not be identified within the WKB approach of Kokkotas & Schutz. Furthermore, we have established that the 'kink' that was a prominent feature of the spectra of Kokkotas & Schutz, but which did not appear in the results of Leins et al., was a numerical artefact. Using our new numerical code we are also able to compute, for the first time, several of the slowly damped (p) modes for the considered stellar models. For very compact stars we find, somewhat surprisingly, that the damping of these modes does not decrease monotonically as one proceeds to higher oscillation frequencies. The existence of low-order modes that damp away much faster than anticipated may have implications for questions regarding stellar stability and the lifetime of gravitational-wave sources. The present results illustrate the accuracy and reliability of the complex-coordinate method and indicate that the method could prove to be of great use also in problems involving rotating stars. There is no apparent reason why the complex-coordinate approach should not extend to rotating stars, whereas it is accepted that all previous methods will fail to do so.
1995
Article
http://edoc.mpg.de/60218
Monthly Notices of the Royal Astronomical Society, v.274, 1039-1048 (1995)
en
oai:edoc.mpg.de:602192009-03-176:82
Reassessment of the reported correlations between gravitational waves and neutrinos associated with SN 1987A
Dickson, C. A.
Schutz, Bernard F.
1995
Article
http://edoc.mpg.de/60219
Physical Review D, v.51, 2644-2668 (1995)
en
oai:edoc.mpg.de:602202009-03-176:82
Sources of Gravitational Radiation for Detectors of the 21st Century
Schutz, Bernard F.
World Scientific
1995
Conference-Paper
http://edoc.mpg.de/60220
Coccia, E. ; Pizella, Guido: Gravitational Wave Experiments: proceedings of the first Edoardo Amalfi Conference, World Scientific, 3-17 (1995)
en
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