Singularity Avoidance in Numerical Black Hole Spacetimes

TL;DR

This paper presents a method for avoiding singularities in numerical black hole simulations by using horizon locking coordinates and a causally respectful finite differencing scheme, enabling long-term stable evolution.

Contribution

Introduces a novel approach combining horizon locking coordinates with a causally consistent finite differencing scheme for stable black hole evolution.

Findings

Black holes can be evolved accurately beyond t=1000M.

The scheme effectively avoids singularities in numerical simulations.

Stable long-term evolution of black holes demonstrated.

Abstract

Spacetime singularities in numerical relativity can be avoided by excising a region of the computational domain from inside the apparent horizon. We report on results of such a scheme that is based on using ({\it i}) a horizon locking coordinate which locks the coordinate system to the geometry, and ({\it ii}) a finite differencing scheme which respects the causal structure of the spacetime. With this technique a black hole can be evolved accurately well beyond $t=1000M$, where $M$ is the black hole mass.