Horizon Boundary Condition for Black Hole Spacetimes

Details Horizon Boundary Condition for Black Hole Spacetimes Horizon Boundary Condition for Black Hole Spacetimes

1994-12-22

arxiv.org/abs/gr-qc/9412069v1

Phys.Rev. D51 (1995) 5562-5578

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

22 pages, LaTeX with RevTeX 3.0 macros, 21 uuencoded gz-compressed postscript figures. Also available at http://jean-luc.ncsa.

Scientific paper

10.1103/PhysRevD.51.5562

It was recently shown that spacetime singularities in numerical relativity could be avoided by excising a region inside the apparent horizon in numerical evolutions. In this paper we report on the details of the implementation of this scheme. The scheme is based on using (1)~a horizon locking coordinate which locks the coordinate system to the geometry, and (2)~a finite differencing scheme which respects the causal structure of the spacetime. We show that the horizon locking coordinate can be affected by a number of shift conditions, such as a ``distance freezing'' shift, an ``area freezing'' shift, an ``expansion freezing'' shift, or the minimal distortion shift. The causal differencing scheme is illustrated with the evolution of scalar fields, and its use in evolving the Einstein equations is studied. We compare the results of numerical evolutions with and without the use of this horizon boundary condition scheme for spherical black hole spacetimes. With the boundary condition a black hole can be evolved accurately well beyond $t=1000 M$, where $M$ is the black hole mass.

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