Excising a boosted rotating black hole with overlapping grids

TL;DR

This paper develops a high-order accurate numerical method using overlapping grids to simulate scalar fields around boosted spinning black holes, enabling stable long-term evolution with excision of singularities.

Contribution

It introduces a fourth order accurate discretization with overlapping grids for scalar fields on boosted spinning black holes, including techniques for boundary handling and stability enhancement.

Findings

High-order accuracy achieved with overlapping grids

Stable long-term evolution demonstrated

Comparison of energy conserving schemes and regularity techniques

Abstract

We use the overlapping grids method to construct a fourth order accurate discretization of a first order reduction of the Klein-Gordon scalar field equation on a boosted spinning black hole blackground in axisymmetry. This method allows us to use a spherical outer boundary and excise the singularity from the domain with a spheroidal inner boundary which is moving with respect to the main grid. We discuss the use of higher order accurate energy conserving schemes to handle the axis of symmetry and compare it with a simpler technique based on regularity conditions. We also compare the single grid long term stability property of this formulation of the wave equation with that of a different first order reduction.