Are moving punctures equivalent to moving black holes?

Jonathan Thornburg, Peter Diener, Denis Pollney, Luciano Rezzolla, Erik Schnetter, Ed Seidel, Ryoji Takahashi
<span title="2007-07-17">2007</span> <i title="IOP Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/j5iizqxt2rainmxg6nfmpg2ds4" style="color: black;">Classical and quantum gravity</a> </i> &nbsp;
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
more &raquo; ... m 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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