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  Are moving punctures equivalent to moving black holes?

Thornburg, J., Diener, P., Pollney, D., Rezzolla, L., Schnetter, E., Seidel, E., et al. (2007). Are moving punctures equivalent to moving black holes? Classical and Quantum Gravity, 24(15), 3911-3918. doi:10.1088/0264-9381/24/15/009.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-49C5-9 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-49C7-5
Genre: Journal Article

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Thornburg, Jonathan1, Author
Diener, Peter, Author
Pollney, Denis2, Author              
Rezzolla, Luciano2, Author              
Schnetter, Erik, Author
Seidel, Edward, Author
Takahashi, Ryoji, Author
Affiliations:
1AEI-Golm, MPI for Gravitational Physics, Max Planck Society, Golm, DE, ou_24008              
2Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24013              

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 Abstract: 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.

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 Dates: 2007
 Publication Status: Published in print
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 Identifiers: eDoc: 318096
Other: arXiv:gr-qc/0701038
DOI: 10.1088/0264-9381/24/15/009
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Title: Classical and Quantum Gravity
Source Genre: Journal
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Pages: - Volume / Issue: 24 (15) Sequence Number: - Start / End Page: 3911 - 3918 Identifier: -