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

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

1997-08-27

arxiv.org/abs/gr-qc/9708067v1

Phys.Rev.D56:6320-6335,1997

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

23 pages RevTeX plus 7 PostScript figures. Submitted to Phys. Rev. D

Scientific paper

10.1103/PhysRevD.56.6320

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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