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, thus providing convincing evidence that moving punctures are indeed equivalent to moving black holes. © 2007 IOP Publishing Ltd.
Publication Source (Journal or Book title)
Classical and Quantum Gravity
Thornburg, J., Diener, P., Pollney, D., Rezzolla, L., Schnetter, E., Seidel, E., & Takahashi, R. (2007). Are moving punctures equivalent to moving black holes?. Classical and Quantum Gravity, 24 (15), 3911-3918. https://doi.org/10.1088/0264-9381/24/15/009