Finite difference schemes for second order systems describing black holes
arXiv:gr-qc/0604010 · doi:10.1103/PhysRevD.73.124008
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.
19 pages, 9 figures
Cited by in corpus (5)
- An explicit harmonic code for black-hole evolution using excision
- Implementation of standard testbeds for numerical relativity
- Constraint-preserving boundary treatment for a harmonic formulation of the Einstein equations
- Outer boundary conditions for Einstein's field equations in harmonic coordinates
- Exact boundary conditions in numerical relativity using multiple grids: scalar field tests