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

Abstract

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 (7)

• Figure 1: Log plot of r.m.s. of the change in the lapse; $\Delta x = 0.4$, $\Delta t = 0.1$. a) $53^3$ grid points, boundary at $20M$. b) $103^3$ grid points, boundary at $40M$.
• Figure 2: Evolution of horizon mass for the same simulations.
• Figure 3: Late time Hamiltonian constraint for runs with different resolutions. The values for the higher resolution runs were multiplied by factors of 4 and 16.
• Figure 4: Log plot of r.m.s. of the change in the lapse for different lapse and shift combinations involving elliptic conditions; $\Delta x = 0.4$, $\Delta t = 0.1$, $35^3$ points, boundary at 13$M$. Run 1: stable ($\Gamma$ freezing without drift, 1+log); run 2: stable ($\Gamma$ freezing without drift, K freezing without drift); run 3: unstable ($\Gamma$ freezing without drift, 1+log, static outer boundaries); run 4: unstable ($\Gamma$ freezing with drift, 1+log); run 5: unstable (minimal distortion, 1+log).
• Figure 5: Runs 1, 2, and 3 of Figure \ref{['fig:srlf_ham']} for run times of up to $t = 3000M$.