Toward stable 3D numerical evolutions of black-hole spacetimes

TL;DR

This paper demonstrates long-term stable 3D numerical simulations of static black holes using hyperbolic formulations and parameter tuning, achieving evolutions lasting about 8000M without gauge adjustments.

Contribution

It introduces a method for stable 3D black hole evolutions by employing growth-rate estimates to fine-tune hyperbolic Einstein equations.

Findings

Stable evolutions lasted about 8000M

Growth-rate estimates effectively guide parameter tuning

Fixed gauge isolates intrinsic stability of equations

Abstract

Three dimensional (3D) numerical evolutions of static black holes with excision are presented. These evolutions extend to about 8000M, where M is the mass of the black hole. This degree of stability is achieved by using growth-rate estimates to guide the fine tuning of the parameters in a multi-parameter family of symmetric hyperbolic representations of the Einstein evolution equations. These evolutions were performed using a fixed gauge in order to separate the intrinsic stability of the evolution equations from the effects of stability-enhancing gauge choices.