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Numerical Evolution of Black Holes with a Hyperbolic Formulation of General Relativity

Mark A. Scheel·Thomas W. Baumgarte·Gregory B. Cook·Stuart L. Shapiro·Saul A. Teukolsky
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Abstract

We describe a numerical code that solves Einstein's equations for a Schwarzschild black hole in spherical symmetry, using a hyperbolic formulation introduced by Choquet-Bruhat and York. This is the first time this formulation has been used to evolve a numerical spacetime containing a black hole. We excise the hole from the computational grid in order to avoid the central singularity. We describe in detail a causal differencing method that should allow one to stably evolve a hyperbolic system of equations in three spatial dimensions with an arbitrary shift vector, to second-order accuracy in both space and time. We demonstrate the success of this method in the spherically symmetric case.

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Mark A. Scheel, Thomas W. Baumgarte, Gregory B. Cook, Stuart L. Shapiro, Saul A. Teukolsky. 1997-08-27. Numerical Evolution of Black Holes with a Hyperbolic Formulation of General Relativity. https://doi.org/10.1103/physrevd.56.6320

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