paper

Horizon Boundary Condition for Black Hole Spacetimes

arXiv:gr-qc/9412069 · doi:10.1103/PhysRevD.51.5562

Abstract

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 , where is the black hole mass.

22 pages, LaTeX with RevTeX 3.0 macros, 21 uuencoded gz-compressed postscript figures. Also available at http://jean-luc.ncsa.uiuc.edu/Papers/ Submitted to Physical Review D

References in corpus (2)

Cited by in corpus (52)