A numerical testbed for singularity excision in moving black hole spacetimes

TL;DR

This paper develops a high-precision numerical testbed for simulating scalar fields around moving black holes, evaluating different algorithms for singularity excision in dynamic spacetimes.

Contribution

It introduces a 3D numerical framework for testing singularity excision methods in moving black hole backgrounds, including high-precision static solutions as benchmarks.

Findings

Some algorithms stable for static black holes become unstable at high boost velocities.

The high-precision static solutions serve as effective benchmarks for 3D simulations.

Comparison of centered and upwind schemes reveals stability differences in dynamic scenarios.

Abstract

We evolve a scalar field in a fixed Kerr-Schild background geometry to test simple $(3+1)$-dimensional algorithms for singularity excision. We compare both centered and upwind schemes for handling the shift (advection) terms, as well as different approaches for implementing the excision boundary conditions, for both static and boosted black holes. By first determining the scalar field evolution in a static frame with a $(1+1)$-dimensional code, we obtain the solution to very high precision. This solution then provides a useful testbed for simulations in full $(3+1)$ dimensions. We show that some algorithms which are stable for non-boosted black holes become unstable when the boost velocity becomes high.