An Implementation of DF-GHG with Application to Spherical Black Hole Excision

TL;DR

This paper introduces a new implementation of the DF-GHG formulation in numerical relativity, enabling more flexible coordinate choices and a robust black hole excision method that outperforms previous approaches in spherical symmetry.

Contribution

It presents a novel DF-excision technique that ensures stable black hole simulations by controlling coordinate lightspeeds, validated through tests and scalar field accretion studies.

Findings

DF-excision is reliable where previous methods fail.

Coordinates with controlled lightspeeds improve black hole excision.

Validation confirms robustness in scalar field accretion scenarios.

Abstract

We present an implementation of the dual foliation generalized harmonic gauge (DF-GHG) formulation within the pseudospectral code bamps. The formalism promises to give greater freedom in the choice of coordinates that can be used in numerical relativity. As a specific application we focus here on the treatment of black holes in spherical symmetry. Existing approaches to black hole excision in numerical relativity are susceptible to failure if the boundary fails to remain outflow. We present a method, called DF-excision, to avoid this failure. Our approach relies on carefully choosing coordinates in which the coordinate lightspeeds are under strict control. These coordinates are then combined with the DF-GHG formulation. After performing a set of validation tests in a simple setting, we study the accretion of large pulses of scalar field matter on to a spherical black hole. We compare the results of DF-excision with a naive setup. DF-excision proves reliable even when the previous approach fails.