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ID: 318096.0, MPI für Gravitationsphysik / Astrophysical Relativity
Are moving punctures equivalent to moving black holes?
Authors:Thornburg, Jonathan; Diener, Peter; Pollney, Denis; Rezzolla, Luciano; Schnetter, Erik; Seidel, Edward; Takahashi, Ryoji
Date of Publication (YYYY-MM-DD):2007
Title of Journal:Classical and Quantum Gravity
Volume:24
Issue / Number:15
Start Page:3911
End Page:3918
Review Status:not specified
Audience:Not Specified
Abstract / Description:When simulating the inspiral and coalescence of a binary black-hole system, special care needs to be taken in handling the singularities. Two main techniques are used in numerical-relativity simulations: A first and more traditional one ``excises'' a spatial neighbourhood of the singularity from the numerical grid on each spacelike hypersurface. A second and more recent one, instead, begins with a ``puncture'' solution and then evolves the full 3-metric, including the singular point. In the continuum limit, excision is justified by the light-cone structure of the Einstein equations and, in practice, can give accurate numerical solutions when suitable discretizations are used. However, because the field variables are non-differentiable at the puncture, there is no proof that the moving-punctures technique is correct, particularly in the discrete case. To investigate this question we use both techniques to evolve a binary system of equal-mass non-spinning black holes. We compare the evolution of two curvature 4-scalars with proper time along the invariantly-defined worldline midway between the two black holes, using Richardson extrapolation to reduce the influence of finite-difference truncation errors. We find that the excision and moving-punctures evolutions produce the same invariants along that worldline, and thus the same spacetimes throughout that worldline's causal past. This provides convincing evidence that moving-punctures are indeed equivalent to moving black holes.
External Publication Status:published
Document Type:Article
Communicated by:Bernhard F. Schutz
Affiliations:MPI für Gravitationsphysik/Astrophysical Relativity
Identifiers:LOCALID:arXiv:gr-qc/0701038
DOI:10.1088/0264-9381/24/15/009
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