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
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- Constraint preserving boundary conditions for the Z4c formulation of general relativity
- Implementation of standard testbeds for numerical relativity
- Numerical stability of the Z4c formulation of general relativity
- Outer boundary conditions for Einstein's field equations in harmonic coordinates
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- Finite Difference Methods for Second Order in Space, First Order in Time Hyperbolic Systems and the Linear Shifted Wave Equation as a Model Problem in Numerical Relativity
- Exact boundary conditions in numerical relativity using multiple grids: scalar field tests