Towards a Singularity-Proof Scheme in Numerical Relativity

TL;DR

This paper introduces a new numerical relativity scheme that excises singularities using horizon-locking coordinates and causal-structure-respecting finite differencing, showing promising results in spherical collapse scenarios.

Contribution

It presents a novel scheme combining horizon-locking coordinates and causal finite differencing to effectively avoid singularities in numerical relativity.

Findings

Successful excision of singularities in spherical collapse

Scheme maintains stability by respecting spacetime causal structure

Encouraging initial results suggest improved numerical relativity simulations

Abstract

Progress in numerical relativity has been hindered for 30 years because of the difficulties of avoiding spacetime singularities in numerical evolution. We propose a scheme which excises a region inside an apparent horizon containing the singularity. Two major ingredients of the scheme are the use of a horizon-locking coordinate and a finite differencing which respects the causal structure of the spacetime. Encouraging results of the scheme in the spherical collapse case are given.