Finite difference schemes for second order systems describing black holes

Details Finite difference schemes for second order systems describing black holes Finite difference schemes for second order systems describing black holes

2006-04-04

arxiv.org/abs/gr-qc/0604010v1

Phys.Rev.D73:124008,2006

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

19 pages, 9 figures

Scientific paper

10.1103/PhysRevD.73.124008

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.

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