Gauge conditions for long-term numerical black hole evolutions without excision

TL;DR

This paper proposes new gauge conditions in numerical relativity that prevent slice stretching, enabling long-term black hole simulations without excision to run over 1000M, significantly exceeding previous limits.

Contribution

It introduces effective lapse and shift conditions that address slice stretching in non-excision black hole evolutions, extending simulation durations substantially.

Findings

Run times increased from 30-40M to over 1000M

Effective gauge conditions prevent slice stretching

Enables stable long-term black hole simulations without excision

Abstract

Numerical relativity has faced the problem that standard 3+1 simulations of black hole spacetimes without singularity excision and with singularity avoiding lapse and vanishing shift fail after an evolution time of around 30-40M due to the so-called slice stretching. We discuss lapse and shift conditions for the non-excision case that effectively cure slice stretching and allow run times of 1000M and more.