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Are moving punctures equivalent to moving black holes?

MPG-Autoren

Thornburg,  Jonathan
AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Pollney,  Denis
Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Rezzolla,  Luciano
Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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0701038v2.pdf
(Preprint), 202KB

cqg7_15_009.pdf
(Verlagsversion), 243KB

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Zitation

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.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-0013-49C5-9
Zusammenfassung
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.