Simple excision of a black hole in 3 + 1 numerical relativity

@article{Alcubierre2001SimpleEO,
  title={Simple excision of a black hole in 3 + 1 numerical relativity},
  author={Miguel Alcubierre and Bernd Bruegmann},
  journal={Physical Review D},
  year={2001},
  volume={63},
  pages={104006}
}
We describe a simple implementation of black hole excision in 3+1 numerical relativity. We apply this technique to a Schwarzschild black hole with octant symmetry in Eddington-Finkelstein coordinates and show how one can obtain accurate, long-term stable numerical evolutions. 

Figures from this paper

Novel finite-differencing techniques for numerical relativity: application to black-hole excision
We use rigorous techniques from numerical analysis of hyperbolic equations in bounded domains to construct stable finite-difference schemes for numerical relativity, in particular for their use in
Improved numerical stability of stationary black hole evolution calculations
We experiment with modifications of the BSSN form of the Einstein field equations (a reformulation of the ADM equations) and demonstrate how these modifications affect the stability of numerical
Modifications for numerical stability of black hole evolution
We experiment with several new modifications for the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation of the Einstein field equations and demonstrate how these modifications affect the stability
Numerical modeling of black holes as sources of gravitational waves in a nutshell
Abstract. These notes summarize basic concepts underlying numerical relativity and in particular the numerical modeling of black hole dynamics as a source of gravitational waves. Main topics are the
Finite difference schemes for second order systems describing black holes
In the harmonic description of general relativity, the principal part of Einstein's equations reduces to 10 curved space wave equations for the components of the space-time metric. We present
Moving black holes via singularity excision
We present a singularity excision algorithm appropriate for numerical simulations of black holes moving throughout the computational domain. The method is an extension of the excision procedure
Toward a dynamical shift condition for unequal mass black hole binary simulations
Moving puncture simulations of black hole binaries rely on a specific gauge choice that leads to approximately stationary coordinates near each black hole. Part of the shift condition is a damping
Binary Black Hole Coalescence
The two-body problem in general relativity is reviewed, focusing on the final stages of the coalescence of the black holes as uncovered by recent successes in numerical solution of the field
Numerical Simulations of Black Hole Formation
Using recent advance in numerical relativity, three-dimensional simula- tions of the formation of black holes through gravitational collapse of rotating stars have been performed with unprecedented
Numerical evolution of multiple black holes with accurate initial data
TLDR
Numerical evolutions of three equal-mass black holes using the moving puncture approach and the results for three black hole evolutions with sixth-order waveform convergence are presented.
...
...