Finite difference schemes for second order systems describing black holes
General Relativity and Quantum Cosmology
2008-11-26 v1
Abstract
In the harmonic description of general relativity, the principle part of Einstein's equations reduces to 10 curved space wave equations for the componenets of the space-time metric. We present theorems regarding the stability of several evolution-boundary algorithms for such equations when treated in second order differential form. The theorems apply to a model black hole space-time consisting of a spacelike inner boundary excising the singularity, a timelike outer boundary and a horizon in between. These algorithms are implemented as stable, convergent numerical codes and their performance is compared in a 2-dimensional excision problem.
Cite
@article{arxiv.gr-qc/0604010,
title = {Finite difference schemes for second order systems describing black holes},
author = {Mohammad Motamed and M. Babiuc and B. Szilagyi and H-O. Kreiss and J. Winicour},
journal= {arXiv preprint arXiv:gr-qc/0604010},
year = {2008}
}
Comments
19 pages, 9 figures