Modeling the Black Hole Excision Problem
arXiv:gr-qc/0412101 · doi:10.1103/PhysRevD.71.104035
Abstract
We analyze the excision strategy for simulating black holes. The problem is modeled by the propagation of quasi-linear waves in a 1-dimensional spatial region with timelike outer boundary, spacelike inner boundary and a horizon in between. Proofs of well-posed evolution and boundary algorithms for a second differential order treatment of the system are given for the separate pieces underlying the finite difference problem. These are implemented in a numerical code which gives accurate long term simulations of the quasi-linear excision problem. Excitation of long wavelength exponential modes, which are latent in the problem, are suppressed using conservation laws for the discretized system. The techniques are designed to apply directly to recent codes for the Einstein equations based upon the harmonic formulation.
21 pages, 14 postscript figures, minor contents update
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Cited by in corpus (12)
- Dynamical Excision Boundaries in Spectral Evolutions of Binary Black Hole Spacetimes
- An explicit harmonic code for black-hole evolution using excision
- Harmonic Initial-Boundary Evolution in General Relativity
- Implementation of standard testbeds for numerical relativity
- AMR, stability and higher accuracy
- Testing numerical relativity with the shifted gauge wave
- Numerical stability for finite difference approximations of Einstein's equations
- Discrete boundary treatment for the shifted wave equation
- Finite difference schemes for second order systems describing black holes
- 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
- Numerical treatment of interfaces for second-order wave equations