2020-10-25T19:03:12Zhttp://edoc.mpg.de/ac_p_oai.ploai:edoc.mpg.de:26992009-03-206:83
Complete null data for a black hole collision
Husa, Sascha
Gomez, Roberto
Winicour, Jeffrey
We discuss a sequence of numerically constructed geometries describing binary black hole event horizons -- providing the necessary input for characteristic evolution of the exterior spacetime. Our sequence approaches a single Schwarzschild horizon as one limiting case and also includes cases where the horizon's crossover surface is not hidden by a marginally anti-trapped surface (MATS).
2001
Article
http://edoc.mpg.de/2699
Physical Review D, v.64, 024010 (2001)
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oai:edoc.mpg.de:27062009-03-206:83
Characteristic Evolution and Matching
Winicour, Jeffrey
I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress is traced from the early stage of 1D feasibility studies to current 3D black codes that simulate binary black holes. A prime application of characteristic evolution is Cauchy-characteristic matching, which is also reviewed.
2001
Article
http://edoc.mpg.de/2706
Living Reviews in Relativity, v.3 (2001)
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oai:edoc.mpg.de:27122009-03-206:83
Asymptotically Flat Initial Data with Prescribed Regularity at Infinity
Dain, Sergio
Friedrich, Helmut
We prove the existence of a large class of asymptotically flat initial data with non-vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space-like infinity in terms of powers of a radial coordinate.
2001
Article
http://edoc.mpg.de/2712
Communications in Mathematical Physics, v.222, 569-609 (2001)
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oai:edoc.mpg.de:27132009-03-206:83
Initial data for two Kerr-like black holes
Dain, Sergio
We prove the existence of a family of initial data for the Einstein vacuum equation which can be interpreted as the data for two Kerr-like black holes in arbitrary location and with spin in arbitrary direction. When the mass parameter of one of them is zero, this family reduces exactly to the Kerr initial data. The existence proof is based on a general property of the Kerr metric which can be used in other constructions as well. Further generalizations are also discussed.
2001
Article
http://edoc.mpg.de/2713
Physical Review Letters, v.87, 121101 (2001)
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oai:edoc.mpg.de:27232009-03-206:83
The Wahlquist-Newman solution
Mars, Marc
Based on a geometrical property which holds both for the Kerr metric and for the Wahlquist metric we argue that the Kerr metric is a vacuum subcase of the Wahlquist perfect-fluid solution. The Kerr-Newman metric is a physically preferred charged generalization of the Kerr metric. We discuss which geometric property makes this metric so special and claim that a charged generalization of the Wahlquist metric satisfying a similar property should exist. This is the Wahlquist-Newman metric, which we present explicitly in this paper. This family of metrics has eight essential parameters and contains the Kerr-Newman-de Sitter and the Wahlquist metrics, as well as the whole Plebanski limit of the rotating C-metric, as particular cases. We describe the basic geometric properties of the Wahlquist-Newman metric, including the electromagnetic field and its sources, the static limit of the family and the extension of the spacetime across the horizon.
2001
Article
http://edoc.mpg.de/2723
Physical Review D, v.63, 064022 (2001)
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oai:edoc.mpg.de:27242009-03-206:83
Spacetime Ehlers group : Transformation law for the Weyl tensor
Mars, Marc
The spacetime Ehlers group, which is a symmetry of the Einstein vacuum field equations for strictly stationary spacetimes, is defined and analyzed in a purely spacetime context (without invoking the projection formalism). In this setting, the Ehlers group finds its natural description within an infinite dimensional group of transformations that maps Lorentz metrics into Lorentz metrics and which may be of independent interest. The Ehlers group is shown to be well defined independently of the causal character of the Killing vector (which may become null on arbitrary regions). We analyze which global conditions are required on the spacetime for the existence of the Ehlers group. The transformation law for the Weyl tensor under Ehlers transformations is explicitly obtained. This allows us to study where, and under which circumstances, curvature singularities in the transformed spacetime will arise. The results of the paper are applied to obtain a local characterization of the Kerr-NUT metric.
2001
Article
http://edoc.mpg.de/2724
Classical and Quantum Gravity, v.18, 719-738 (2001)
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oai:edoc.mpg.de:27252009-03-206:83
On the uniqueness of the Einstein-Straus model
Mars, Marc
We show that the Einstein-Straus model does not give a robust answer to the problem of the influence of the cosmic expansion on the local physics. This is done by finding the most general static region embeddable in a Friedman-Lemaitre-Robertson-Walker expanding cosmology and showing that the model must be almost spherically symmetric. More precisely, we show that the boundary of the static region must be a two-sphere at each instant of cosmic time. The motion of this two-sphere in spacetime is as follows: its would-be center (if there was no static region) moves along a path whose projection on any 3-space of constant cosmic time is a geodesic with respect to the induced 3-metric. The velocity of this geodesic is determined from the matching. In particular, this center must be at rest with respect to the cosmologic flow (thus giving a spherically symmetric model) when any of the standard energy-momentum tensors inside the static region is imposed.
2001
Article
http://edoc.mpg.de/2725
Classical and Quantum Gravity, v.18, 3645-3663 (2001)
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oai:edoc.mpg.de:27292009-03-206:83
Manufacture of Gowdy spacetimes with spikes
Rendall, Alan D.
Weaver, Marsha
In numerical studies of Gowdy spacetimes evidence has been found for the development of localized features (''spikes') involving large gradients near the singularity. The rigorous mathematical results available up to now did not cover this kind of situation. In this work we show the existence of large classes of Gowdy spacetimes exhibiting features of the kind discovered numerically. These spacetimes are constructed by applying certain transformations to previously known spacetimes without spikes. It is possible to control the behaviour of the Kretschmann scalar near the singularity in detail. This curvature invariant is found to blow up in a way which is non-uniform near the spike in some cases. When this happens it demonstrates that the spike is a geometrically invariant feature and not an artefact of the choice of variables used to parametrize the metric. We also identify another class of spikes which are artefacts. The spikes produced by our method are compared with the results of numerical and heuristic analyses of the same situation.
2001
Article
http://edoc.mpg.de/2729
Classical and Quantum Gravity, v.18, 2959-2975 (2001)
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oai:edoc.mpg.de:27302009-03-206:83
The future asymptotics of Bianchi VIII vacuum solutions
Ringström, Hans
Bianchi VIII vacuum solutions to Einstein's equations are causally geodesically complete to the future, given an appropriate time orientation, and the objective of this paper is to analyse the asymptotic behaviour of solutions in this time direction. For the Bianchi class A spacetimes, there is a formulation of the field equations that was presented in an article by Wainwright and Hsu, and we will analyse the asymptotic behaviour of solutions in these variables. We also try to give the analytic results a geometric interpretation by analysing how a normalized version of the Riemannian metric on the spatial hypersurfaces of homogeneity evolves
2001
Article
http://edoc.mpg.de/2730
Classical and Quantum Gravity, v.18, 3791-3823 (2001)
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oai:edoc.mpg.de:27332009-04-066:83
Oscillatory approach the singularity in vacuum spacetimes with T2 isometry
Berger, Beverly K.
Isenberg, James
Weaver, Marsha
We use qualitative arguments combined with numerical simulations to argue that, in the approach to the singularity in a vacuum solution of Einstein's equations with T2 isometry, the evolution at a generic point in space is an endless succession of Kasner epochs, punctuated by bounces in which either a curvature term or a twist term becomes important in the evolution equations for a brief time. Both curvature bounces and twist bounces may be understood within the context of local mixmaster dynamics although the latter have never been seen before in spatially inhomogeneous cosmological spacetimes.
2001
Article
http://edoc.mpg.de/2733
Physical Review D, v.64, 084006 (2001)
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oai:edoc.mpg.de:27362009-03-206:83
On blowup for Yang-Mills fields
Bizon, Piotr
Tabor, Z.
We study development of singularities for the spherically symmetric Yang-Mills equations in $d+1$ dimensional Minkowski spacetime for $d=4$ (the critical dimension) and $d=5$ (the lowest supercritical dimension). Using combined numerical and analytical methods we show in both cases that generic solutions starting with sufficiently large initial data blow up in finite time. The mechanism of singularity formation depends on the dimension: in $d=5$ the blowup is exactly self-similar while in $d=4$ the blowup is only approximately self-similar and can be viewed as the adiabatic shrinking of the marginally stable static solution. The threshold for blowup and the connection with critical phenomena in the gravitational collapse (which motivated this research) are also briefly discussed.
2001
Article
http://edoc.mpg.de/2736
Physical Review D, v.64, 121701 (2001)
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oai:edoc.mpg.de:27412009-04-276:83
Boundary conditions in linearized harmonic gravity
Szilagyi, Bela
Schmidt, Bernd
Winicour, Jeffrey
We investigate the initial-boundary value problem for linearized gravitational theory in harmonic coordinates. Rigorous techniques for hyperbolic systems are applied to establish well-posedness for various reductions of the system into a set of six wave equations. The results are used to formulate computational algorithms for Cauchy evolution in a 3-dimensional bounded domain. Numerical codes based upon these algorithms are shown to satisfy tests of robust stability for random constraint violating initial data and random boundary data; and shown to give excellent performance for the evolution of typical physical data. The results are obtained for plane boundaries as well as piecewise cubic spherical boundaries cut out of a Cartesian grid.
2002
Article
http://edoc.mpg.de/2741
Physical Review D, v.65 (2002)
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oai:edoc.mpg.de:27432009-03-206:83
Conserved quantities in a black hole collision
Dain, Sergio
Valiente-Kroon, Juan Antonio
The Newman-Penrose constants of the spacetime corresponding to the development of the Brill-Lindquist initial data are calculated by making use of a particular representation of spatial infinity due to H Friedrich. The Brill-Lindquist initial data set represents the head-on collision of two non-rotating black holes. In this case one non-zero constant is obtained. Its value is given in terms of the product of the individual masses of the black holes and the square of a distance parameter separating the two black holes. This constant retains its value all along null infinity, and therefore it provides information about the late time evolution of the collision process. In particular, it is argued that the magnitude of the constants provides information about the amount of residual radiation contained in the spacetime after the collision of the black holes.
2002
Article
http://edoc.mpg.de/2743
Classical and Quantum Gravity, v.19, 811-815 (2002)
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oai:edoc.mpg.de:27442009-03-206:83
Can one detect a non-smooth null infinity?
Valiente-Kroon, Juan Antonio
It is shown that the precession of a gyroscope can be used to elucidate the nature of the smoothness of the null infinity of an asymptotically flat spacetime (describing an isolated body). A model is proposed for which the effects of precession in the non-smooth null infinity case are of the order r-2ln r. In contrast, in the smooth version the effects are of the order r-3. This difference should provide an effective criterion to decide on the nature of the smoothness of null infinity.
2001
Article
http://edoc.mpg.de/2744
Classical and Quantum Gravity, v.18, 4311-4316 (2001)
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oai:edoc.mpg.de:27452009-05-266:83
Bondi-type systems near space-like infinity and the calculation of the NP-constants
Friedrich, Helmut
Kannar, Janos
We relate Bondi systems near spacelike infinity to another type of gauge conditions. While the former are based on null infinity, the latter are defined in terms of Einstein propagation, the conformal structure, and data on some Cauchy hypersurface. For a certain class of time symmetric space-times we study an expansion which allows us to determine the behavior of various fields arising in Bondi systems in the region of space-time where null infinity touches spacelike infinity. The coefficients of these expansions can be read off from the initial data. We obtain, in particular, expressions for the constants discovered by Newman and Penrose in terms of the initial data. For this purpose we calculate a certain expansion introduced by Friedrich [J. Geom. Phys. 24, 83-163 (1998)] up to third order. (C) 2000 American Institute of Physics. [S0022-2488(00)02602-5].
2000
Article
http://edoc.mpg.de/2745
Journal of Mathematical Physics, v.41, 2195-2232 (2000)
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oai:edoc.mpg.de:27482009-03-206:83
Initial data for stationary spacetimes near spacelike infinity
Dain, Sergio
We study Cauchy initial data for asymptotically flat, stationary vacuum spacetimes near spacelike infinity. The fall-off behaviour of the intrinsic metric and the extrinsic curvature is characterized. We prove that they have an analytic expansion in powers of a radial coordinate. The coefficients of the expansion are analytic functions of the angles. This result allow us to fill a gap in the proof found in the literature of the statement that all asymptotically flat, vacuum stationary spacetimes admit an analytic compactification at null infinity. Stationary initial data are physically important and highly non-trivial examples of a large class of data with similar regularity properties at spacelike infinity, namely, initial data for which the metric and the extrinsic curvature have asymptotic expansion in terms of powers of a radial coordinate. We isolate the property of the stationary data which is responsible for this kind of expansion.
2001
Article
http://edoc.mpg.de/2748
Classical and Quantum Gravity, v.18, 4329-4338 (2001)
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oai:edoc.mpg.de:27542009-03-206:83
Gravitational lensing in spherically symmetric static spacetimes with centrifugal force reversal
Hasse, Wolfgang
Perlick, Volker
In Schwarzschild spacetime the value r = 3m of the radius coordinate is characterized by three different properties: (a) there is a ?light sphere,? (b) there is ?centrifugal force reversal,? (c) it is the upper limiting radius for a non-transparent Schwarzschild source to act as a gravitational lens that produces infinitely many images. In this paper we prove a theorem to the effect that these three properties are intimately related in any spherically symmetric static spacetime. We illustrate the general results with some examples including black-hole spacetimes and Morris-Thorne wormholes.
2002
Article
http://edoc.mpg.de/2754
General Relativity and Gravitation, v.34, 415-433 (2002)
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oai:edoc.mpg.de:27592009-03-206:83
Fuchsian analysis of S^2xS^1 and S^3 Gowdy spacetimes
Stahl, Fredrik
The Gowdy spacetimes are vacuum solutions of the Einstein equations with two commuting Killing vectors having compact spacelike orbits with T3, S2 × S1 or S3 topology. In the case of T3 topology, Kichenassamy and Rendall have found a family of singular solutions which are asymptotically velocity dominated by construction. In the case when the velocity is between 0 and 1, the solutions depend on the maximal number of free functions. We consider the similar case with S2 × S1 or S3 topology, where the main complication is the presence of symmetry axes. The results for T3 may be applied locally except at the axes, where one of the Killing vectors degenerates. We use Fuchsian techniques to show the existence of singular solutions similar to the T3 case. We first solve the analytic case and then generalize to the smooth case by approximating smooth data with a sequence of analytic data. However, for the metric to be smooth at the axes, the velocity must be -1 or 3 there, which is outside the range where the constructed solutions depend on the full number of free functions. A plausible explanation is that in general a spiky feature may develop at the axis, a situation which is unsuitable for a direct treatment by Fuchsian methods.
2002
Article
http://edoc.mpg.de/2759
Classical and Quantum Gravity, v.19, 4483-4504 (2002)
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oai:edoc.mpg.de:27602009-03-206:83
Global Prescribed Mean Curvature foliations in cosmological spacetimes I
Henkel, Oliver
This work investigates some global questions about cosmological space-times with two-dimensional spherical, plane, and hyperbolic symmetry containing "well-behaved" matter. The result is that these space-times admit a global foliation by prescribed mean curvature surfaces, which extends at least toward a crushing singularity. The time function of the foliation is geometrically defined and unique up to the choice of an initial Cauchy surface. This work generalizes a similar analysis on constant mean curvature foliations and avoids the topological obstructions arising from the existence problem. (C) 2002 American Institute of Physics.
2002
Article
http://edoc.mpg.de/2760
Journal of Mathematical Physics, v.43, 2439-2465 (2002)
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oai:edoc.mpg.de:27612009-03-206:83
Global Prescribed Mean Curvature foliations in cosmological spacetimes II
Henkel, Oliver
This paper is devoted to the investigation of global properties of prescribed mean curvature (PMC) foliations in cosmological space-times with local U(1)xU(1) symmetry and matter described by the Vlasov equation. It turns out that these space-times admit a global foliation by PMC surfaces as well, but the techniques to achieve this goal are more complex than in the cases considered in Paper I [Henkel (2002)]
2002
Article
http://edoc.mpg.de/2761
Journal of Mathematical Physics, v.43, 2466-2485 (2002)
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oai:edoc.mpg.de:27622009-03-206:83
Schwarzschild horizon and the gravitational redshift formula
Malec, Edward
The gravitational redshift formula is usually derived in the geometric optics approximation. In this paper we consider an exact formulation of the problem in the Schwarzschild spacetime, with the intention of clarifying under what conditions this redshift law is valid. It is shown that in the case of shocks, the radial component of the Poynting vector can scale according to the redshift formula, under a suitable condition. If that condition is not satisfied, then the effect of backscattering can lead to significant modifications. The results obtained imply that the energy flux of the short wavelength radiation obeys the standard gravitational redshift formula while the energy flux of long waves can scale differently, with redshifts being dependent on the frequency.
2002
Article
http://edoc.mpg.de/2762
Classical and Quantum Gravity, v.19, 571-577 (2002)
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oai:edoc.mpg.de:27642009-03-206:83
Accelerated sources in de Sitter spacetime and the insufficiency of retarded fields
Bicak, Jiri
Krtous, Pavel
The scalar and electromagnetic fields produced by the geodesic and uniformly accelerated discrete charges in de Sitter spacetime are constructed by employing the conformal relation between de Sitter and Minkowski space. Special attention is paid to new effects arising in spacetimes which, like de Sitter space, have spacelike conformal infinities. Under the presence of particle and event horizons, purely retarded fields (appropriately defined) become necessarily singular or even cannot be constructed at the "creation light cones"?future light cones of the "points" at which the sources "enter" the universe. We construct smooth (outside the sources) fields involving both retarded and advanced effects, and analyze the fields in detail in case of (i) scalar monopoles, (ii) electromagnetic monopoles, and (iii) electromagnetic rigid and geodesic dipoles.
2001
Article
http://edoc.mpg.de/2764
Physical Review D, v.64, 124020 (2001)
oai:edoc.mpg.de:27722009-03-206:83
Initial data for fluid bodies in general relativity
Dain, Sergio
Nagy, Gabriel
We show that there exist asymptotically flat almost-smooth initial data for the Einstein?perfect-fluid equation that represent an isolated liquid-type body. By liquid-type body we mean that the fluid energy density has compact support and takes a strictly positive constant value at its boundary. By almost-smooth we mean that all initial data fields are smooth everywhere on the initial hypersurface except at the body boundary, where tangential derivatives of any order are continuous at that boundary.
2002
Article
http://edoc.mpg.de/2772
Physical Review D, v.65, 084020 (2002)
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oai:edoc.mpg.de:27752009-03-206:83
A New Tradition between Discrete and Contiuous Self-Similarity in Critical Gravitational Collapse
Lechner, Christiane
Thornburg, Jonathan
Husa, Sascha
Aichelburg, Peter C.
We analyze a bifurcation phenomenon associated with critical gravitational collapse in a family of self-gravitating SU(2) sigma models. As the dimensionless coupling constant decreases, the critical solution changes from discretely self-similar (DSS) to continuously self-similar (CSS). Numerical results provide evidence for a bifurcation which is analogous to a heteroclinic loop bifurcation in dynamical systems, where two fixed points (CSS) collide with a limit cycle (DSS) in phase space as the coupling constant tends to a critical value.
2002
Article
http://edoc.mpg.de/2775
Physical Review D, v.65 (2002)
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oai:edoc.mpg.de:27762009-03-206:83
Book Review : The Universe. Visions and Perspectives
Winicour, Jeffrey
I review the collection of essays which the editors Naresh Dadich and Ajit Kembhavi have assembled as a festschrift to honor Jayant Narlikar.
2002
Article
http://edoc.mpg.de/2776
General Relativity and Gravitation, v.34, 1327-1329 (2002)
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oai:edoc.mpg.de:27772009-03-206:83
Cosmological models and centre manifold theory
Rendall, Alan D.
Centre manifold theory is applied to some dynamical systems arising from spatially homogeneous cosmological models. Detailed information is obtained concerning the late-time behaviour of solutions of the Einstein equations of Bianchi type III with collisionless matter. In addition some statements in the literature on solutions of the Einstein equations coupled to a massive scalar field are proved rigorously.
2002
Article
http://edoc.mpg.de/2777
General Relativity and Gravitation, v.34, 1277-1294 (2002)
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oai:edoc.mpg.de:27802009-03-206:83
Retarded radiation from colliding black holes in the close limit
Husa, Sascha
Zlochower, Yosef
Gomez, Roberto
Winicour, Jeffrey
We use null hypersurface techniques in a new approach to calculate the retarded waveform from a binary black hole merger in the close approximation. The process of removing ingoing radiation from the system leads to two notable features in the shape of the close approximation waveform for a head-on collision of black holes: (i) an initial quasinormal ringup and (ii) weak sensitivity to the parameter controlling the collision velocity. Feature (ii) is unexpected and has the potential importance of enabling the design of an efficient template for extracting the gravitational wave signal from the noise.
2002
Article
http://edoc.mpg.de/2780
Physical Review D, v.65 (2002)
en
oai:edoc.mpg.de:27812009-03-206:83
Simplified models of electromagnetic and gravitational radiation damping
Kunze, Markus
Rendall, Alan D.
In previous work the authors have analysed the global properties of an approximate model of radiation damping for charged particles. This work is put into context and related to the original motivation of understanding approximations used in the study of gravitational radiation damping. We examine to what extent the results obtained previously depend on the particular model chosen. Comparisons are made with other models for gravitational and electromagnetic fields. The relation of the kinetic model for which theorems were proved to certain many-particle models with radiation damping is exhibited
2001
Article
http://edoc.mpg.de/2781
Classical and Quantum Gravity, v.18, 3573-3587 (2001)
en
oai:edoc.mpg.de:27862009-03-206:83
Quiscent cosmological singularities
Andersson, Lars
Rendall, Alan D.
The most detailed existing proposal for the structure of spacetime singularities originates in the work of Belinskii, Khalatnikov and Lifshitz. We show rigorously the correctness of this proposal in the case of analytic solutions of the Einstein equations coupled to a scalar field or stiff fluid. More specifically, we prove the existence of a family of spacetimes depending on the same number of free functions as the general solution which have the asymptotics suggested by the Belinskii-Khalatnikov-Lifshitz proposal near their singularities. In these spacetimes a neighbourhood of the singularity can be covered by a Gaussian coordinate system in which the singularity is simultaneous and the evolution at different spatial points decouples.
2001
Article
http://edoc.mpg.de/2786
Communications in Mathematical Physics, v.218, 479-511 (2001)
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oai:edoc.mpg.de:27872009-03-206:83
Local and global existence theorems for the Einstein equations
Rendall, Alan D.
This article is a guide to the literature on existence theorems for the Einstein equations which also draws attention to open problems in the field. The local in time Cauchy problem, which is relatively well understood, is treated first. Next global results for solutions with symmetry are discussed. A selection of results from Newtonian theory and special relativity which offer useful comparisons is presented. This is followed by a survey of global results in the case of small data and results on constructing spacetimes with given singularity structure. The article ends with some miscellaneous topics connected with the main theme.
2000
Article
http://edoc.mpg.de/2787
Living Reviews in Relativity, v.3 (2000)
en
oai:edoc.mpg.de:27882003-02-136:83oai:edoc.mpg.de:27912009-04-066:83
Dual Group Actions on C*-Algebras and Their Description by Hilbert Extensions
Baumgärtel, Hellmut
Lledo, Fernando
Given a C*-algebra $A$, a discrete abelian group $X$ and a homomorphism $Theta: X o$ Out$A$ defining the dual action group $Gammasubset$ aut$A$, the paper contains results on existence and characterization of Hilbert ${A,Gamma}$, where the action is given by $hat{X}$. They are stated at the (abstract) C*-level and can therefore be considered as a refinement of the extension results given for von Neumann algebras for example by Jones [Mem.Am.Math.Soc. 28 Nr 237 (1980)] or Sutherland [Publ.Res.Inst.Math.Sci. 16 (1980) 135]. A Hilbert extension exists iff there is a generalized 2-cocycle. These results generalize those in [Commun.Math.Phys. 15 (1969) 173], which are formulated in the context of superselection theory, where it is assumed that the algebra $A$ has a trivial center, i.e. $Z=C1$. In particular the well-known ''''outer characterization'' of the second cohomology $H^2(X,{cal U}(Z),alpha_X)$ can be reformulated: there is a bijection to the set of all $A$-module isomorphy classes of Hilbert extensions. Finally, a Hilbert space representation (due to Sutherland in the von Neumann case) is mentioned. The C*-norm of the Hilbert extension is expressed in terms of the norm of this representation and it is linked to the so-called regular representation appearing in superselection theory.
2002
Article
http://edoc.mpg.de/2791
Mathematische Nachrichten, v.239-240, 11-27 (2002)
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oai:edoc.mpg.de:27922009-03-206:83
Conformal covariance of massless free nets
Lledo, Fernando
In the present paper we review in a fibre bundle context the covariant and massless canonical representations of the Poincare' group as well as certain unitary representations of the conformal group (in 4 dimensions). We give a simplified proof of the well-known fact that massless canonical representations with discrete helicity extend to unitary and irreducible representations of the conformal group mentioned before. Further we give a simple new proof that massless free nets for any helicity value are covariant under the conformal group. Free nets are the result of a direct (i.e. independent of any explicit use of quantum fields) and natural way of constructing nets of abstract C*-algebras indexed by open and bounded regions in Minkowski space that satisfy standard axioms of local quantum physics. We also give a group theoretical interpretation of the embedding ${got I}$ that completely characterizes the free net: it reduces the (algebraically) reducible covariant representation in terms of the unitary canonical ones. Finally, as a consequence of the conformal covariance we also mention for these models some of the expected algebraic properties that are a direct consequence of the conformal covariance (essential duality, PCT--symmetry etc.).
2001
Article
http://edoc.mpg.de/2792
Reviews in Mathematical Physics, v.13, 1135-1161 (2001)
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oai:edoc.mpg.de:27982009-03-206:83
Fuchsian analysis of singularities in Gowdy spacetimes beyond analyticity
Rendall, Alan D.
Fuchsian equations provide a way of constructing large classes of spacetimes whose singularities can be described in detail. In some of the applications of this technique only the analytic case could be handled up to now. This paper develops a method of removing the undesirable hypothesis of analyticity. This is applied to the specific case of the Gowdy spacetimes in order to show that analogues of the results known in the analytic case hold in the smooth case. As far as possible the likely strengths and weaknesses of the method, as applied to more general problems, are displayed.
2000
Article
http://edoc.mpg.de/2798
Classical and Quantum Gravity, v.17, 3305-3316 (2000)
en
oai:edoc.mpg.de:28052009-04-066:83
Dynamics of spatially homogeneous locally rotationally symmetric solutions of the Einstein-Vlasov equations
Rendall, Alan D.
Uggla, Claes
The dynamics of the Einstein-Vlasov equations for a class of cosmological models with four Killing vectors is discussed in the case of massive particles. It is shown that in all models analysed the solutions with massive particles are asymptotic to solutions with massless particles at early times. It is also shown that in Bianchi types I and II the solutions with massive particles are asymptotic to dust solutions at late times. That Bianchi type III models are also asymptotic to dust solutions at late times is consistent with our results but is not established by them.
2000
Article
http://edoc.mpg.de/2805
Classical and Quantum Gravity, v.17, 4697-4714 (2000)
en
oai:edoc.mpg.de:30362009-03-206:83
New conformally flat initial data for spinning black holes
Dain, Sergio
Lousto, Carlos O.
Takahashi, Ryoji
We obtain an explicit solution of the momentum constraint for conformally flat, maximal slicing, initial data which gives an alternative to the purely longitudinal extrinsic curvature of Bowen and York. The new solution is related, in a precise form, with the extrinsic curvature of a Kerr slice. We study these new initial data representing spinning black holes by numerically solving the Hamiltonian constraint. They have the following features: (i) they contain less radiation, for all allowed values of the rotation parameter, than the corresponding single spinning Bowen-York black hole; (ii) the maximum rotation parameter J/m(2) reached by this solution is higher than that of the purely longitudinal solution, allowing us thus to describe holes closer to a maximally rotating Kerr one. We discuss the physical interpretation of these properties and their relation with the weak cosmic censorship conjecture. Finally, we generalize the data for multiple black holes using the "puncture" and isometric formulations
2002
Article
http://edoc.mpg.de/3036
Physical Review D, v.65 (2002)
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oai:edoc.mpg.de:30402009-03-206:83
Kasner-like behaviour for subcritical Einstein-matter systems
Damour, Thibault
Henneaux, Marc
Rendall, Alan D.
Weaver, Marsha
Confirming previous heuristic analyses \''a la Belinskii-Khalatnikov-Lifshitz, it is rigorously proven that certain ''''subcritical Einstein-matter systems exhibit a monotone, generalized Kasner behaviour in the vicinity of a spacelike singularity. The D-dimensional coupled Einstein-dilaton-p-form system is subcritical if the dilaton couplings of the p-forms belong to some dimension dependent open neighbourhood of zero, while pure gravity is subcritical if D is greater than or equal to 11. Our proof relies, like the recent theorem dealing with the (always subcritical) Einstein-dilaton system, on the use of Fuchsian techniques, which enable one to construct local, analytic solutions to the full set of equations of motion. The solutions constructed are ''''general in the sense that they depend on the maximal expected number of freefunctions.
2002
Article
http://edoc.mpg.de/3040
Annales Henri Poincare, 1049-1111 (2002)
en
oai:edoc.mpg.de:30422009-03-196:83
Static, Self-Gravitating Elastic Bodies
Schmidt, Bernd G.
Beig, Robert
There is proved an existence theorem, in the Newtonian theory, for static, self-gravitating bodies composed of elastic material. The theorem covers the case where these bodies are small, but allows them to have arbitrary shape.
2003
Article
http://edoc.mpg.de/3042
Proceedings of the Royal Society of London A, v.459, 109-115 (2003)
en
oai:edoc.mpg.de:30442009-03-206:83
Theorems on existence and global dynamics for the Einstein equations
Rendall, Alan D.
This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity that offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section
2002
Article
http://edoc.mpg.de/3044
Living Reviews in Relativity, v.5 (2002)
en
oai:edoc.mpg.de:30472009-03-206:83
Asymptotically flat and regular Cauchy data
Dain, Sergio
I describe the construction of a large class of asymptotically flat initial data with non-vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space-like infinity in terms of powers of a radial coordinate. I emphasize the motivations and the main ideas behind the proofs.
Springer, Lecture Notes in Physics
2002
InBook
http://edoc.mpg.de/3047
The conformal structure of space time : geometry, analysis, numerics, 161-181 (2002)
en
oai:edoc.mpg.de:30482009-03-206:83
Polyhomogheneous expansions close to null and spatial infinity
Valiente-Kroon, Juan Antonio
A study of the linearised gravitational field (spin 2 zero-rest-mass field) on a Minkowski background close to spatial infinity is done. To this purpose, a certain representation of spatial infinity in which it is depicted as a cylinder is used. A first analysis shows that the solutions generically develop a particular type of logarithmic divergence at the sets where spatial infinity touches null infinity. A regularity condition on the initial data can be deduced from the analysis of some transport equations on the cylinder at spatial infinity. It is given in terms of the linearised version of the Cotton tensor and symmetrised higher order derivatives, and it ensures that the solutions of the transport equations extend analytically to the sets where spatial infinity touches null infinity. It is later shown that this regularity condition together with the requirement of some particular degree of tangential smoothness ensures logarithm-free expansions of the time development of the linearised gravitational field close to spatial and null infiniti
Springer
2002
InBook
http://edoc.mpg.de/3048
The conformal structure of space time : geometry, analysis, numerics, 135-159 (2002)
en
oai:edoc.mpg.de:30522009-03-206:83
Conformal geodesics on vacuum space-times
Friedrich, Helmut
We discuss properties of conformal geodesics on general, vacuum, and warped product space-times and derive a system of conformal deviation equations. The results are used to show how to construct on the Schwarzschild-Kruskal space-time global conformal Gauss coordinates which extends smoothly and without degeneracy to future and past null infinity.
2002
Article
http://edoc.mpg.de/3052
Communications in Mathematical Physics, v.235, 513-543 (2002)
en
oai:edoc.mpg.de:30682009-03-206:83
Problems and Successes in the Numerical Approach to theConformal Field Equations
Husa, Sascha
This talk reports on the status of an approach to the numerical study of isolated systems with the conformal field equations. We first describe the algorithms used in a code which has been developed at the AEI in the last years, and discuss a milestone result obtained by Hübner.
Then we present more recent results as examples to sketch the problems we face in the conformal approach to numerical relativity and outline a possible roadmap toward making this approach a practical tool.
Springer
2002
InBook
http://edoc.mpg.de/3068
Frauendiener, Jörg; Friedrich, Helmut: The conformal structure of space time : geometry, analysis, numerics, 239-259 (2002)
oai:edoc.mpg.de:30692009-03-196:83
Numerical relativity with the conformal field equations
Husa, Sascha
I discuss the conformal approach to the numerical simulation of radiating isolated systems in general relativity. The method is based on conformal compactification and a reformulation of the Einstein equations in terms of rescaled variables, the so-called ''''conformal field equations developed by Friedrich. These equations allow to include ''''infinity on a finite grid, solving regular equations, whose solutions give rise to solutions of the Einstein equations of (vacuum) general relativity. The conformal approach promises certain advantages, in particular with respect to the treatment of radiation extraction and boundary conditions. I will discuss the essential features of the analytical approach to the problem, previous work on the problem -- in particular a code for simulations in 3+1 dimensions, some new results, open problems and strategies for future work
Springer
2003
Conference-Paper
http://edoc.mpg.de/3069
Fernández-Jambrina, Leonardo; González-Romero, Luis Manuel: Current Trends in Relativistic Astrophysics: Theoretical, Numerical, Observational, Springer, 159-192 (2003)
en
oai:edoc.mpg.de:30842009-03-196:83
Early radiative properties of the developments of time symmetric, conformally flat initial data
Valiente-Kroon, Juan Antonio
Using a representation of spatial infinity based in the properties of conformal geodesics, the first terms of an expansion for the Bondi mass for the development of time symmetric, conformally flat initial data are calculated. As it is to be expected, the Bondi mass agrees with the ADM at the sets where null infinity 'touches' spatial infinity. The second term in the expansion is proportional to the sum of the squared norms of the Newman-Penrose constants of the spacetime. In base of this result it is argued that these constants may provide a measure of the incoming radiation contained in the spacetime. This is illustrated by means of the Misner and Brill-Lindquist data se
2003
Article
http://edoc.mpg.de/3084
Classical and Quantum Gravity, v.20, L53-L59 (2003)
en
oai:edoc.mpg.de:30942009-03-206:83
Black Hole Interaction Energy
Dain, Sergio
The interaction energy between two black holes at a large separation distance is calculated. The first term in the expansion corresponds to the Newtonian interaction between the masses. The second term corresponds to the spin-spin interaction. The calculation is based on the interaction energy defined on the two black holes' initial data. No test particle approximation is used. The relation between this formula and cosmic censorship is discussed.
2002
Article
http://edoc.mpg.de/3094
Physical Review D, v.66 (2002)
en
oai:edoc.mpg.de:31072009-03-206:83
Gravitational redshifts in electromagnetic bursts occuring near Schwarzschild horizon
Karkowski, Janusz
Malec, Edward
It was suggested earlier that the gravitational redshift formula can be invalid when the effect of the backscattering is strong. It is demonstrated here, for an exemplary electromagnetic pulse that is: i) initially located very close to the horizon of a Schwarzschild black hole and ii) strongly backscattered, that a mean frequency does not obey the standard redshift formula. Redshifts appear to depend on the frequency and there manifests a backscatter-induced blueshift in the outgoing radiation.
2002
Article
http://edoc.mpg.de/3107
Classical and Quantum Gravity, v.20, 85-91 (2002)
en
oai:edoc.mpg.de:31082009-03-206:83
Waves in Schwarzschild spacetimes: how strong can be imprints of the spacetime curvature
Karkowski, Janusz
Roskkowski, K.
Swierczynski, Z.
Malec, Edward
An emitted radiation can be reprocessed in curved spacetimes, due to the breakdown of the Huyghens principle. A maximization procedure for the energy diffusion allows one to obtain wave packets (gravitational and electromagnetic) that are particularly strongly backscattered. Examples are shown with the backscattered part exceeding by one order remnants of initial signals. A robust ringing can be observed, with amplitudes exceeding leftovers of the main radiation pulse. The analysis of the obtained results allows one to set demands on some parameters in the numerical description of a realistic process of the collapse of two black holes
2002
Article
http://edoc.mpg.de/3108
Physical Review D, v.67 (2002)
en
oai:edoc.mpg.de:31152009-03-206:83
Energy inequalities for isolated systems and hypersurfaces moving by their curvature
Huisken, Gerhard
Ilmanen, Tom
The total energy of an isolated gravitating system in General Relativity is described by a geometric invariant of asymptotically flat Riemannian 3--manifolds. One--parameter families of two-dimensional hypersurfaces foliating such a manifold and obeying natural curvature conditions can be used to encode and study geometrical and physical properties of the 3--manifold such as mass, quasi-local mass, the center of mass and energy inequalities. The article describes recent results on Penrose inequalities, inverse mean curvature flow, constant mean curvature surfaces and their interconnections.
World Scientific
2002
Conference-Paper
http://edoc.mpg.de/3115
Nigel T. Bishop and Sunil D. Maharaj: Proceedings of the 16th International Conference on General Relativity and Gravitation, World Scientific, 162-173 (2002)
en
oai:edoc.mpg.de:31182009-03-206:83
The Fields of Uniformly Accelerated Charges in de Sitter Spacetime
Bicak, Jiri
Krtous, Pavel
The scalar and electromagnetic fields of charges uniformly accelerated in de Sitter spacetime are constructed. They represent the generalization of the Born solution describing fields of two particles with hyberbolic motion in flat spacetime. In the limit Lambda->0, the Born solutions are retrieved. Since in de Sitter universe the infinities I(+/-) are spacelike, the radiative properties of the fields depend on the way in which a given point of I(+/-) is approached. The fields must involve both retarded and advanced effects: Purely retarded fields do not satisfy the constraints at the past infinity I(-)
2002
Article
http://edoc.mpg.de/3118
Physical Review Letters, v.88 (2002)
en
oai:edoc.mpg.de:31192009-03-196:83
On Gowdy vacuum spacetimes
Ringström, Hans
By Fuchsian techniques, a large family of Gowdy vacuum spacetimes have been constructed for which one has detailed control over the asymptotic behaviour. In this paper we formulate a condition on initial data yielding the same form of asymptotics.
2004
Article
http://edoc.mpg.de/3119
Mathematical Proceedings of the Cambridge Philosophical Society, v.136, 485-512 (2004)
en
oai:edoc.mpg.de:31332009-03-196:83
Existence of CMC and constant areal time foliations in T^2 symmetric spacetimes with Vlasov matter
Andreasson, Hakan
Rendall, Alan D.
Weaver, Marsha
The global structure of solutions of the Einstein equations coupled to the Vlasov equation is investigated in the presence of a two-dimensional symmetry group. It is shown that there exist global CMC and areal time foliations. The proof is based on long-time existence theorems for the partial differential equations resulting from the Einstein-Vlasov system when conformal or areal coordinates are introduced.
2004
Article
http://edoc.mpg.de/3133
Communications in Partial Differential Equations, v.29, 237-262 (2004)
en
oai:edoc.mpg.de:31342009-03-206:83
Well-Posed Initial-Boundary Evolution in General Relativity
Szilagyi, Bela
Winicour, Jeffrey
The technique of maximally dissipative boundary conditions is applied to establish a simple, well-posed version of the general relativistic initial-boundary value problem for the reduced Einstein equations in harmonic coordinates. The method is implemented as a nonlinear evolution code which satisfies several convergence tests in the nonlinear regime and is robustly stable in the weak field regime. A linearized version has been stably matched to a characteristic code to compute the gravitational waveform radiated to infinity.
2003
Article
http://edoc.mpg.de/3134
Physical Review D, v.68 (2003)
en
oai:edoc.mpg.de:31352009-03-196:83
Global Small Solutions of the Vlasov-Maxwell System in Absence of Incoming Radiation
Calogero, Simon
We consider a modified version of the Vlasov-Maxwell system in which the usual Maxwell fields are replaced by their retarded parts. We show that solutions of this modified system exist globally for a small number of particles and that they describe a system without incoming radiation
2004
Article
http://edoc.mpg.de/3135
Indiana University Mathematics Journal, v.53, 1331-1363 (2004)
en
oai:edoc.mpg.de:31722009-03-196:83
Relativistic Elasticity
Schmidt, Bernd G.
Beig, Robert
Relativistic elasticity on an arbitrary spacetime is formulated as a Lagrangian field theory which is covariant under spacetime diffeomorphisms. This theory is the relativistic version of classical elasticity in the hyperelastic, materially frame-indifferent case and, on Minkowski space, reduces to the latter in the non-relativistic limit . The field equations are cast into a first -- order symmetric hyperbolic system. As a consequence one obtains local--in--time existence and uniqueness theorems under various circumstances
2003
Article
http://edoc.mpg.de/3172
Classical and Quantum Gravity, v.20, 889-904 (2003)
en
oai:edoc.mpg.de:31772009-03-206:83
Neuere Entwicklungen der relativistischen Physik
Jürgen, Ehlers
Pössel, Markus
Neuausgabe des klassischen Anfänger-Lehrbuchs von Max Born, herausgegeben und mit Ergänzungskapiteln zu neueren Entwicklungen der Relativitätstheorie versehen von J. Ehlers und M. Pössel
Springer
2001
InBook
http://edoc.mpg.de/3177
Born, Max: Die Relativitätstheorie Einsteins., 325-470 (2001)
de
oai:edoc.mpg.de:31782009-03-206:83
Colliding black holes from a null point of view: the close limit
Husa, Sascha
Campanelli, Manuela
Gomez, Roberto
Winicour, Jeffrey
Zlochower, Yosef
We present a characteristic algorithm for computing the perturbations of a Schwarzschild spacetime by means of solving the Teukolsky equations. Our methods and results are expected to have direct bearing on the study of binary black holes presently underway using a fully {em nonlinear} characteristic code cite{Gomez98a}
2001
Conference-Paper
http://edoc.mpg.de/3178
Proceedings of 9th Marcel Grossmann meeting (MG9) (2001)
en
oai:edoc.mpg.de:32032009-06-116:83
Gravitationslinsen - Lichtablenkung in Schwerefeldern und ihre Anwendungen
Ehlers, Jürgen
Carl Friedrich von Siemens Stiftung
1999
InBook
http://edoc.mpg.de/3203
Ehlers, Jürgen
de
oai:edoc.mpg.de:32042009-03-206:83
The Cauchy Problem for the Einstein Equations
Friedrich, Helmut
Rendall, Alan D.
Springer
2000
InBook
http://edoc.mpg.de/3204
Einstein's field equations and their physical implications : selected essays in honour of Jürgen Ehlers, 127-224 (2000)
en
oai:edoc.mpg.de:32112009-03-206:83
Blow-up for solutions of hyperbolic PDE and spacetime singularities
Rendall, Alan D.
An important question in mathematical relativity theory is that of the nature of spacetime singularities. The equations of general relativity, the Einstein equations, are essentially hyperbolic in nature and the study of spacetime singularities is naturally related to blow-up phenomena for nonlinear hyperbolic systems. These connections are explained and recent progress in applying the theory of hyperbolic equations in this field is presented. A direction which has turned out to be fruitful is that of constructing large families of solutions of the Einstein equations with singularities of a simple type by solving singular hyperbolic systems. Heuristic considerations indicate, however, that the generic case will be much more complicated and require different techniques.
Groupement de Recherche 1151 du CNRS
2000
InBook
http://edoc.mpg.de/3211
Proceedings of Journees "Equations aux Derivees Partielles", 1-12 (2000)
en
oai:edoc.mpg.de:32122009-03-206:83
On the propagation of jump discontinuities in relativistic cosmology
van Elst, Henk
Ellis, George F. R.
Schmidt, Bernd G.
A recent dynamical formulation at a derivative level partial derivative (3)g for fluid spacetime geometries (M,g,u), that employs the concept of evolution systems in a first-order symmetric hyperbolic format, implies the existence in the Weyl curvature branch of a set of timelike characteristic three-surfaces associated with the propagation speed upsilon = 1/2 relative to fluid-comoving observers. We show it is a physical role of the constraint equations to prevent realization of jump discontinuities in the derivatives of the related initial data so that Weyl curvature modes propagating along these three-surfaces cannot be activated. In addition we introduce a new, illustrative first-order symmetric hyperbolic evolution system at a derivative level partial derivative (2)g for baryotropic perfect fluid cosmological models that are invariant under the transformation of an Abelian G(2) isometry group.
2000
Article
http://edoc.mpg.de/3212
Physical Review D, v.62 (2000)
en
oai:edoc.mpg.de:32172009-03-206:83
Local Quantum Constraints
Grundling, Hendrik
Lledo, Fernando
We analyze the situation of a local quantum field theory with constraints, both indexed by the same set of space-time regions. In particular we find "weak"Haag-Kastler axioms which will ensure that the final constrained theory satisfies the usual Haag-Kastler axioms. Gupta-Bleuler electromagnetism is developed indetail as an example of a theory which satisfies the "weak" Haag-Kastler axioms but not the usual ones. This analysis is done by pure C*-algebraic means without employing any indefinite metric representations, and we obtain the same physical algebra and positive energy representation for it than by the usual means. The price for avoiding the indefinite metric, is the use of nonregular representations and complex valued test functions. We also exhibit the precise connection with the usual indefinite metric representation. We conclude the analysis by comparing the final physical algebra produced by a system of local constrainings with the one obtained from a single global constraining and also consider the issue of reduction by stages. For the usual spectral condition on the generators of the translation group, we also find a "weak" version, and show that the Gupta-Bleuler example satisfies it.
2000
Article
http://edoc.mpg.de/3217
Reviews in Mathematical Physics, v.12, 1159-1218 (2000)
en
oai:edoc.mpg.de:32202009-03-206:83
Black holes in the brane world: Time symmetric initial data
Shiromizu, Tetsuya
Shibata, Masaru
We numerically construct time-symmetric initial data sets of a black hole in the Randall-Sundrum brane world model, assuming that the black hole is spherical on the brane. We find that the apparent horizon is cigar-shaped in the 5D spacetime.
2000
Article
http://edoc.mpg.de/3220
Physical Review D, v.62 (2000)
en
oai:edoc.mpg.de:32362009-03-206:83
Charged Brane-World Black Holes
Chamblin, Andrew
Reall, Harvey S.
Shinkai, Hisa-aki
Shiromizu, Tetsuya
We study charged brane-world black holes in the model of Randall and Sundrum in which our universe is viewed as a domain wall in asymptotically anti-de Sitter space. Such black holes can carry two types of "charge", one arising from the bulk Weyl tensor and one from a gauge field trapped on the wall. We use a combination of analytical and numerical techniques to study how these black holes behave in the bulk. It has been shown that a Reissner-Nordstrom geometry is induced on the wall when only Weyl charge is present. However, we show that such solutions exhibit pathological features in the bulk. For more general charged black holes, our results suggest that the extent of the horizon in the fifth dimension is usually less than for an uncharged black hole that has the same mass or the same horizon radius on the wall.
2001
Article
http://edoc.mpg.de/3236
Physical Review D, v.63 (2001)
en
oai:edoc.mpg.de:33142009-03-206:83
Global properties of gravitational lens maps in a Lorentzian manifold setting
Perlick, Volker
In a general-relativistic spacetime (Lorentzian manifold), gravitational lensing can be characterized by a lens map, in analogy to the lens map of the quasi-Newtonian approximation formalism. The lens map is defined on the celestial sphere of the observer (or on part of it) and it takes values in a two-dimensional manifold representing a two-parameter family of worldlines. In this article we use methods from differential topology to characterize global properties of the lens map. Among other things, we use the mapping degree (also known as Brouwer degree) of the lens map as a tool for characterizing the number of images in gravitational lensing situations. Finally, we illustrate the general results with gravitational lensing (a) by a static string, (b) by a spherically symmetric body, (c) in asymptotically simple and empty spacetimes, and (d) in weakly perturbed Robertson-Walker spacetimes.
2001
Article
http://edoc.mpg.de/3314
Communications in Mathematical Physics, v.220, 403-428 (2001)
en
oai:edoc.mpg.de:33342009-03-206:83
On the existence of global solutions for T 3-Gowdy spacetimes with stringy matter
Narita, Makoto
We show a global existence theorem for the Einstein-matter equations of T3-Gowdy symmetric spacetimes with stringy matter. The areal time coordinate is used. It is shown that this spacetime has a crushing singularity into the past. From these results we can show that the spacetime is foliated by compact hypersurfaces of constant mean curvature.
2002
Article
http://edoc.mpg.de/3334
Classical and Quantum Gravity, v.19, 6279-6288 (2002)
en
oai:edoc.mpg.de:33492009-03-206:83
Numerical Calculation of Conformally Smooth Hyperboloidal Data
Hübner, Peter
This is the third paper in a series describing a numerical implementation of the conformal Einstein equation. This paper describes a scheme to calculate (three-)dimensional data for the conformal field equations from a set of free functions. The actual implementation depends on the topology of the spacetime. We discuss the implementation and exemplary calculations for data leading to spacetimes with one spherical null infinity (asymptotically Minkowski) and for data leading to spacetimes with two toroidal null infinities (asymptotically A3). We also outline the (technical) modifications of the implementation needed to calculate data for spacetimes with two and more spherical null infinities (asymptotically Schwarzschild and asymptotically multiple black holes).
2001
Article
http://edoc.mpg.de/3349
Classical and Quantum Gravity, v.18, 1421-1440 (2001)
en
oai:edoc.mpg.de:33532009-03-206:83
From Now to Timelike Infinity on a Finite Grid
Hübner, Peter
We use the conformal approach to numerical relativity to evolve hyperboloidal gravitational wave data without any symmetry assumptions. Although our grid is finite in space and time, we cover the whole future of the initial data in our calculation, including future null and future timelike infinity.
2001
Article
http://edoc.mpg.de/3353
Classical and Quantum Gravity, v.18, 1871-1884 (2001)
en
oai:edoc.mpg.de:33572009-03-206:83
An application of the DR-duality theory for compact groups to endomorphism categories of C*-algebras with nontrivial center
Baumgärtel, Hellmut
Lledo, Fernando
In Rev. Math. Phys. 4 (1997) 785 we study Hilbert-C* systems {F,G} where the fixed point algebra A has nontrivial center Z and where A'cap F=Z is satisfied. The corresponding category of all canonical endomorphisms of A contains characteristic mutually isomorphic subcategories of the Doplicher/Roberts-type which are connected with the choice of distinguished G-invariant algebraic Hilbert spaces within the corresponding G-invariant Hilbert Z-modules. We present in this paper the solution of the corresponding inverse problem. More precisely, assuming that the given endomorphism category T of a C*-algebra A with center Z contains a certain subcategory of the DR-type, a Hilbert extension {F,G} of A is constructed such that T is isomorphic to the category of all canonical endomorphisms of A w.r.t. {F,G} and A'cap F=Z. Furthermore, there is a natural equivalence relation between admissible subcategories and it is shown that two admissible subcategories yield A-module isomorphic Hilbert extensions iff they are equivalent. The essential step of the solution is the application of the standard DR-theory to the assigned subcategory.
American Mathematical Society
2001
Conference-Paper
http://edoc.mpg.de/3357
Longo, Roberto: Mathematical physics in mathematics and physics : quantum and operator algebraic aspects, American Mathematical Society, 1-10 (2001)
en
oai:edoc.mpg.de:33592009-03-206:83
The Vlasov-Poisson system with radiation damping
Kunze, Markus
Rendall, Alan D.
We set up and analyze a model of radiation damping within the framework of continuum mechanics, inspired by a model of post-Newtonian hydrodynamics due to Blanchet, Damour and Schaefer. In order to simplify the problem as much as possible we replace the gravitational field by the electromagnetic field and the fluid by kinetic theory. We prove that the resulting system has a well-posed Cauchy problem globally in time for general initial data and in all solutions the fields decay to zero at late times. In particular, this means that the model is free from the runaway solutions which frequently occur in descriptions of radiation reaction.
2001
Article
http://edoc.mpg.de/3359
Annales Henri Poincare, v.2, 857-886 (2001)
en
oai:edoc.mpg.de:33602009-03-206:83
The Bianchi IX attractor
Ringström, Hans
We consider the asymptotic behaviour of spatially homogeneous spacetimes of Bianchi type IX close to the singularity (we also consider some of the other Bianchi types, e. g. Bianchi VIII in the stiff fluid case). The matter content is assumed to be an orthogonal perfect fluid with linear equation of state and zero cosmological constant. In terms of the variables of Wainwright and Hsu, we have the following results. In the stiff fluid case, the solution converges to a point for all the Bianchi class A types. For the other matter models we consider, the Bianchi IX solutions generically converge to an attractor consisting of the closure of the vacuum type II orbits. Furthermore, we observe that for all the Bianchi class A spacetimes, except those of vacuum Taub type, a curvature invariant is unbounded in the incomplete directions of inextendible causal geodesics.
2001
Article
http://edoc.mpg.de/3360
Annales Henri Poincare, v.2, 405-500 (2001)
en
oai:edoc.mpg.de:33672009-03-206:83
Classification of image distortions in terms of Petrov types
Chrobok, Thoralf
Perlick, Volker
An observer surrounded by sufficiently small spherical light sources at a fixed distance will see a pattern of elliptical images distributed over the sky, owing to the distortion effect (shearing effect) of the spacetime geometry upon light bundles. In lowest non-trivial order with respect to the distance, this pattern is completely determined by the conformal curvature tensor (Weyl tensor) at the observation event. In this paper we derive formulas that allow to calculate these distortion patterns in terms of the Newman-Penrose formalism. Then we represent the distortion patterns graphically for all Petrov types, and we discuss their dependence on the velocity of the observer.
2001
Article
http://edoc.mpg.de/3367
Classical and Quantum Gravity, v.18, 3059-3079 (2001)
en
oai:edoc.mpg.de:33692009-05-286:83
Type II Critical Collapse of a Self-Gravitating Nonlinear Sigma Model
Husa, Sascha
Lechner, Christiane
Pürrer, Michael
Thornburg, Jonathan
Aichelburg, Peter C.
We report on the existence and phenomenology of type II critical collapse within the one-parameter family of SU(2) sigma models coupled to gravity. Numerical investigations in spherical symmetry show discretely self-similar (DSS) behavior at the threshold of black hole formation for values of the dimensionless coupling constant eta ranging from 0.2 to 100; at 0.18 we see small deviations from DSS. While the echoing period Delta of the critical solution rises sharply towards the lower limit of this range, the characteristic mass scaling has a critical exponent gamma which is almost independent of eta, asymptoting to 0.1185ą0.0005 at large eta. We also find critical scaling of the scalar curvature for near-critical initial data. Our numerical results are based on an outgoingnull-cone formulation of the Einstein-matter equations, specialized to spherical symmetry. Our numerically computed initial-data critical parameters p* show second order convergence with the grid resolution, and after compensating for this variation in p*, our individual evolutions are uniformly second order convergent even very close to criticality.
2000
Article
http://edoc.mpg.de/3369
Physical Review D, v.62 (2000)
en
oai:edoc.mpg.de:33702009-03-206:83
SU(2) Cosmological Solitons
Lechner, Christiane
Aichelburg, Peter C.
Husa, S.
We present a class of numerical solutions to the SU(2) nonlinear sigma model coupled to the Einstein equations with a cosmological constant Lambda>=0 in spherical symmetry. These solutions are characterized by the presence of a regular static region which includes a center of symmetry. They are parametrized by a dimensionless "coupling constant" beta, the sign of the cosmological constant, and an integer "excitation number" n. The phenomenology we find is compared to the corresponding solutions found for the Einstein-Yang-Mills (EYM) equations with a positive Lambda (EYMLambda). If we choose Lambda positive and fix n, we find a family of static spacetimes with a Killing horizon for 0<=beta<betamax. As a limiting solution for beta= betamax we find a globally static spacetime with Lambda= 0, the lowest excitation being the Einstein static universe. To interpret the physical significance of the Killing horizon in the cosmological context, we apply the concept of a trapping horizon as formulated by Hayward. For small values of beta an asymptotically de Sitter dynamic region contains the static region within a Killing horizon of cosmological type. For strong coupling the static region contains an "eternal cosmological black hole."
2000
Article
http://edoc.mpg.de/3370
Physical Review D, v.62 (2000)
en
oai:edoc.mpg.de:33722009-03-206:83
Time-Independent Gravitational Fields
Beig, Robert
Schmidt, Bernd G.
This article reviews, from a global point of view, rigorous results on time independent spacetimes. Throughout attention is confined to isolated bodies at rest or in uniform rotation in an otherwise empty universe. The discussion starts from first principles and is, as much as possible, self-contained.
Springer
2000
InBook
http://edoc.mpg.de/3372
Einstein's field equations and their physical implications : selected essays in honour of Jürgen Ehlers, 325-372 (2000)
en
oai:edoc.mpg.de:33742009-03-206:83
Foundations of Gravitational Lens Theory
Ehlers, Jürgen
The main concepts of gravitational lens theory are introduced on the basis of spacetime geometry without assuming approximations. The singularities of light cones, in particular their caustics, are reviewed as examples of singularities of Lagrangian resp. Legendrian maps. It is indicated how the usual approximate lens theory may be derived from the general framework.
2000
Article
http://edoc.mpg.de/3374
Annalen der Physik, v.9, 307-330 (2000)
en
oai:edoc.mpg.de:33752009-03-206:83
The Theory of Caustics and Wave Front Singularities with Physical Applications
Ehlers, Jürgen
Newman, Ezra T.
This is intended as an introduction to and review of the theory of Lagrangian and Legendrian submanifolds and their associated maps developed by Arnold and his collaborators. The theory is illustrated by applications to HamiltonJacobi theory and the eikonal equation, with an emphasis on null surfaces and wave fronts and their associated caustics and singularities.
2000
Article
http://edoc.mpg.de/3375
Journal of Mathematical Physics, v.41, 3344-3378 (2000)
en
oai:edoc.mpg.de:33762009-03-206:83
General Relativity and Gravitation
Ehlers, Jürgen
Macmillan Publishers Ltd.
2001
InBook
http://edoc.mpg.de/3376
urn:ISBN:0-333-75088-8
info:doi/10.1888/0333750888/2108
Encyclopedia of Astronomy and Astrophysics Vol.2, 966-971 (2001)
en
oai:edoc.mpg.de:33992009-03-196:83
Type II Critical Phenomena of a Self-Gravitating Nonlinear Sigma Model
Lechner, Christiane
Thornburg, Jonathan
Husa, Sascha
Aichelburg, Peter C.
2003
Conference-Paper
http://edoc.mpg.de/3399
Lobo, A.; Fayos, F.; Garriga, J.; Gaztanaga, E.; Verdaguer, E.: Proceedings of the Spanish Relativity Meeting (ERE 2002), 229-233 (2003)
en
oai:edoc.mpg.de:34002009-03-206:83
Data for the Numerical Calculation of the Kruskal Space-Time
Schmidt, Bernd G.
Springer
2002
InBook
http://edoc.mpg.de/3400
The conformal structure of space time: geometry, analysis, numerics, 283-296 (2002)
en
oai:edoc.mpg.de:34012009-03-206:83
Conformal Einstein evolution
Friedrich, Helmut
We discuss various properties of the conformal field equations and their consequences for the asymptotic structure of space-times.
Springer
2002
InBook
http://edoc.mpg.de/3401
The conformal structure of space time: geometry, analysis, numerics, 1-50 (2002)
en
oai:edoc.mpg.de:34422009-03-206:83
John Lighton Synge, FRS - Short biography
Ehlers, Jürgen
2002
Article
http://edoc.mpg.de/3442
General Relativity and Gravitation, v.34, 2174-2175 (2002)
en
oai:edoc.mpg.de:34432009-03-206:83
Relativistic hydrodynamics
Ehlers, Jürgen
2002
Article
http://edoc.mpg.de/3443
General Relativity and Gravitation, v.34, 2171-2174 (2002)
en
oai:edoc.mpg.de:34442009-03-206:83
Aber Jordan war der Erste
Ehlers, Jürgen
Schücking, Engelbert
2002
Article
http://edoc.mpg.de/3444
Physik Journal, v.11, 71-72 (2002)
de
oai:edoc.mpg.de:34452009-03-206:83
Aktuelle Probleme der Gravitationsphysik
Ehlers, Jürgen
Während Einsteins Gravitationstheorie, die Allgemeine Relativitätstheorie, nach spektakulären Anfangserfolgen zwischen 1915 und 1919 für lange Zeit ein vom Hauptstrom der physikalischen Forschung getrenntes Gebiet blieb, gelang es ab 1960, mehrere ihrer Voraussagen durch Beobachtungen und Experimente mit wachsender Genauigkeit zu überprüfen. In den letzten 30 Jahren ist die Allgemeine Relativitätstheorie zu einem integralen Bestandteil der Astrophysik geworden. Ein aktuelles Forschungsgebiet betrifft Gravitationslinsen, und der direkte Nachweis von Gravitationswellen wird mit Spannung erwarte
2002
Article
http://edoc.mpg.de/3445
Physik Journal, v.7, 43-43 (2002)
de
oai:edoc.mpg.de:35172009-03-206:83
Applications of the theory of evolution equations to general relativity
Rendall, Alan D.
World Scientific
2002
Conference-Paper
http://edoc.mpg.de/3517
Bishop, Nigel T.; Maharaj, Sunil D.: General Relativity and Gravitation, World Scientific, 276-293 (2002)
en
oai:edoc.mpg.de:35192009-03-206:83
Adiabatic Vacuum States on General Spacetime Manifolds: Definition, Construction, and Physical Properties
Junker, Wolfgang
Schrohe, Elmar
Adiabatic vacuum states are a well-known class of physical states for linear quantum fields on Robertson-Walker spacetimes. We extend the definition of adiabatic vacua to general spacetime manifolds by using the notion of the Sobolev wavefront set. This definition is also applicable to interacting field theories. Hadamard states form a special subclass of the adiabatic vacua. We analyze physical properties of adiabatic vacuum representations of the Klein-Gordon field on globally hyperbolic spacetime manifolds (factoriality, quasiequivalence, local definiteness, Haag duality) and construct them explicitly, if the manifold has a compact Cauchy surface
2002
Article
http://edoc.mpg.de/3519
Annales Henri Poincare, v.3, 1113-1181 (2002)
en
oai:edoc.mpg.de:35222009-03-206:83
Selected Solutions of Einsteins Field Equations: Their Role in General Relativity and Astrophysics
Bicak, Jiri
Springer
2000
InBook
http://edoc.mpg.de/3522
Einsteins Field Equations and Their Physical Implications, 1-126 (2000)
en
oai:edoc.mpg.de:35262009-03-196:83
On the Einstein-Vlasov system with hyperbolic symmetry
Andreasson, Hakan
Rein, Gerhard
Rendall, Alan D.
It is shown that a spacetime with collisionless matter evolving from data on a compact Cauchy surface with hyperbolic symmetry can be globally covered by compact hypersurfaces on which the mean curvature is constant and by compact hypersurfaces on which the area radius is constant. Results for the related cases of spherical and plane symmetry are reviewed and extended. The prospects of using the global time coordinates obtained in this way to investigate the global geometry of the spacetimes concerned are discussed
2003
Article
http://edoc.mpg.de/3526
Mathematical Proceedings of the Cambridge Philosophical Society, v.134, 529-549 (2003)
en
oai:edoc.mpg.de:35302009-03-196:83
Regularizing a Singular Special Lagrangian Variety
Butscher, Adrian
Suppose M1 and M2 are two special Lagrangian submanifolds of Rtn with boundary that intersect transversally at one point p. The set M1 cup M2 is a singular special Lagrangian variety with an isolated singularity at the point of intersection. Suppose further that the tangent planes at the intersection satisfy an angle condition (which always holds in dimension n=3). Then, M1 cup M2 is regularizable; in other words, there exists a family of smooth, minimal Lagrangian submanifolds M(alpha) with boundary that converges to M1cup M2 in a suitable topology. This result is obtained by first gluing a smooth neck into a neighbourhood of M1 cap M2 and then by perturbing this approximate solution until it becomes minimal and Lagrangian
2004
Article
http://edoc.mpg.de/3530
Communications in Analysis and Geometry, v.12, 733-791-733-791 (2004)
en
oai:edoc.mpg.de:35312009-03-196:83
Deformations of Minimal Lagrangian Submanifolds with Boundary
Butscher, Adrian
Let Lbe a special Lagrangian submanifold of a compact, Calabi-Yau manifold Mwith boundary lying on the symplectic, codimension 2 submanifold W. It is shown how deformations of L which keep the boundary of L confined to W can be described by an elliptic boundary value problem, and two results about minimal Lagrangian submanifolds with boundary are derived using this fact. The first is that the space of minimal Lagrangian submanifolds near L with boundary on W is found to be finite dimensional and is parametrised over the space of harmonic 1-forms of L satisfying Neumann boundary conditions. The second is that if W is a symplectic, codimension 2 submanifold sufficiently near W then under suitable conditions, there exists a minimal Lagrangian submanifold L near L with boundary on W
2003
Article
http://edoc.mpg.de/3531
Proceedings of the American Mathematical Society, v.131, 1953-1964 (2003)
en
oai:edoc.mpg.de:35362009-03-206:83
Exploring the Conformal Constraint Equations
Butscher, Adrian
One method of studying the asymptotic structure of spacetime is to apply Penrose's conformal rescaling technique. In this setting, the Einstein equations for the metric and the conformal factor in the unphysical spacetime degenerate where the conformal factor vanishes, namely at the boundary representing null infinity. This problem can be avoided by means of a technique of H. Friedrich, which replaces the Einstein equations in the unphysical spacetime by an equivalent system of equations which is regular at the boundary. The initial value problem for these equations produces a system of constraint equations known as the conformal constraint equations. This work describes some of the properties of the conformal constraint equations and develops a perturbative method of generating solutions near flat space under certain simplifying assumptions
Springer
2002
InBook
http://edoc.mpg.de/3536
The conformal structure of space time: geometry, analysis, numerics, 195-222 (2002)
en
oai:edoc.mpg.de:35372009-03-206:83
Semiglobal Numerical Calculations of Asymptotically Minkowski Spacetimes
Husa, Sascha
This talk reports on recent progress toward the semiglobal study of asymptotically flat spacetimes within numerical relativity. The development of a 3D solver for asymptotically Minkowski-like hyperboloidal initial data has rendered possible the application of Friedrich's conformal field equations to astrophysically interesting spacetimes. As a first application, the whole future of a hyperboloidal set of weak initial data has been studied, including future null and timelike infinity. Using this example we sketch the numerical techniques employed and highlight some of the unique capabilities of the numerical code. We conclude with implications for future work
American Institute of Physics
2001
Conference-Paper
http://edoc.mpg.de/3537
Wheeler, J. Craig; Martel, Hugo: Proceedings of Relativistic Astrophysics: 20th Texas Symposium, American Institute of Physics, 734-739 (2001)
en
oai:edoc.mpg.de:236852009-03-206:83
Gravitational waves from a fissioning white hole
Gomez, Roberto
Husa, Sascha
Lehner, Luis
Winicour, Jeffrey
We present a fully nonlinear calculation of the waveform of the gravitational radiation emitted in the fission of a vacuum white hole. At early times, the waveforms agree with close approximation perturbative calculations but they reveal dramatic time and angular dependence in the nonlinear regime. The results pave the way for a subsequent computation of the radiation emitted after a binary black hole merger.
2002
Article
http://edoc.mpg.de/23685
Physical Review D, v.66 (2002)
en
oai:edoc.mpg.de:237132009-03-196:83
A new class of obstructions to the smoothness of null infinity
Valiente-Kroon, Juan Antonio
Expansions of the gravitational field arising from the development of asymptotically Euclidean, time symmetric, conformally flat initial data are calculated in a neighbourhood of spatial and null infinities up to order 6. To this ends a certain representation of spatial infinity as a cylinder is used. This set up is based on the properties of conformal geodesics. It is found that these expansions suggest that null infinity has to be non-smooth unless the Newman-Penrose constants of the spacetime, and some other higher order quantities of the spacetime vanish. As a consequence of these results it is conjectured that similar conditions occur if one were to take the expansions to even higher orders. Furthermore, the smoothness conditions obtained suggest that if a time symmetric initial data which is conformally flat in a neighbourhood of spatial infinity yields a smooth null infinity, then the initial data must in fact be Schwarzschildean around spatial infinity.
2004
Article
http://edoc.mpg.de/23713
Communications in Mathematical Physics, v.244, 133-156 (2004)
en
oai:edoc.mpg.de:237212008-02-206:83
Perturbative Solutions of the Extended Constraint Equations in General Relativity
Butscher, Adrian
The extended constraint equations arise as a special case of the conformal constraint equations that are satisfied by an initial data hypersurface $Z$ in an asymptotically simple spacetime satisfying the vacuum conformal Einstein equations developed by H. Friedrich. The extended constraint equations consist of a quasi-linear system of partial differential equations for the induced metric, the second fundamental form and two other tensorial quantities defined on $Z$, and are equivalent to the usual constraint equations that $Z$ satisfies as a spacelike hypersurface in a spacetime satisfying Einstein's vacuum equation. This article develops a method for finding perturbative, asymptotically flat solutions of the extended constraint equations in a neighbourhood of the flat solution on Euclidean space. This method is fundamentally different from the `classical' method of Lichnerowicz and York that is used to solve the usual constraint equations.
2007
Article
http://edoc.mpg.de/23721
info:doi/10.1007/s00220-007-0204-8
Communications in Mathematical Physics, v.272, 1-23 (2007)
en
oai:edoc.mpg.de:508842009-03-196:83
Global existence and asymptotic behaviour in the future for the Einstein-Vlasov system with positive cosmological constant
Tchapnda, Sophonie Blaise
Rendall, Alan D.
The behaviour of expanding cosmological models with collisionless matter and a positive cosmological constant is analysed. It is shown that under the assumption of plane or hyperbolic symmetry the area radius goes to infinity, the spacetimes are future geodesically complete, and the expansion becomes isotropic and exponential at late times. This proves a form of the cosmic no hair theorem in this class of spacetimes.
2003
Article
http://edoc.mpg.de/50884
Classical and Quantum Gravity, v.20, 3037-3049 (2003)
en
oai:edoc.mpg.de:508892009-03-196:83
Mode coupling in the nonlinear response of black holes
Zlochower, Yosef
Gomez, Roberto
Husa, Sascha
Lehner, Luis
Winicour, Jeffrey
We model the nonlinear generation of waveforms from an excited non-spinning black hole. The results exhibit several important features. When compared to the results obtained by a linearized approximation, we observe large phase shifts, a stronger than linear generation of gravitational output and considerable generation of radiation in polarization states (which are not found in the linearized approximation). Additionally, the amplitudes of modes generated by nonlinear effects have simple scaling properties which can be utilized in an economical way to produce a waveform catalogue.
2003
Article
http://edoc.mpg.de/50889
Physical Review D, v.68 (2003)
en
oai:edoc.mpg.de:509432009-03-196:83
Spin-2 fields on Minkowski space near space-like and null infinity
Friedrich, Helmut
We show that the spin-2 equations on Minkowski space in the gauge of the 'regular finite initial value problem at spacelike infinity' imply estimates which, together with the transport equations on the cylinder at spacelike infinity, allow us to obtain for a large class of initial data information on the smoothness of the solution near spacelike and null infinity of any desired precision.
2003
Article
http://edoc.mpg.de/50943
Classical and Quantum Gravity, v.20, 101-117 (2003)
en
oai:edoc.mpg.de:509462009-03-196:83
A numerical relativistic model of a massive particle in orbit near a Schwarzschild black hole
Bishop, Nigel T.
Gomez, Roberto
Husa, Sascha
Lehner, Luis
We present a method for computing the evolution of a spacetime containing a massive particle and a black hole. The essential idea is that the gravitational field is evolved using full numerical relativity, with the particle generating a non-zero source term in the Einstein equations. The matter fields are not evolved by hydrodynamic equations. Instead the particle is treated as a rigid body whose center follows a geodesic. The necessary theoretical framework is developed and then implemented in a computer code that uses the null-cone, or characteristic, formulation of numerical relativity. The performance of the code is illustrated in test runs, including a complete orbit (near r = 9M) of a Schwarzschild black hole.
2003
Article
http://edoc.mpg.de/50946
Physical Review D, v.68 (2003)
en
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