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Authors: Jonathan Thornburg, Peter Diener, Denis Pollney, Luciano Rezzolla, Erik Schnetter, Ed Seidel, Ryoji Takahashi

Date: Fri, 5 Jan 2007

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 neighborhood 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. While the first approach is mathematically and numerically well-defined, the second one still maintains a non-differentiable point within the black hole. No strong-field evidence has yet been provided to show that the two approaches are indeed dynamically equivalent. To address this question we have used both techniques to evolve a binary system of equal-mass non-spinning black holes and compared the evolution of two curvature 4-scalars with proper time along the invariantly-defined worldline midway between the two black holes. Using Richardson-extrapolation techniques to reduce the influence of the finite-difference truncation error, we find that the moving-punctures and excision evolutions produce the same spacetimes along that worldline. This represents the first strong-field and dynamical evidence that the moving-puncture prescription is robust both mathematically and numerically.

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