Improved numerical stability of stationary black hole evolution calculations

TL;DR

This paper explores modifications to the BSSN formulation of Einstein's equations to enhance the numerical stability of black hole simulations, achieving accurate evolutions of rotating and non-rotating black holes without symmetry constraints.

Contribution

It introduces specific modifications to the BSSN equations that improve stability in black hole evolution calculations, enabling longer and more accurate simulations.

Findings

Stable simulations for black holes with J/M up to 0.9M

Effective use of excision in various symmetry setups

Enhanced numerical stability of the BSSN formulation

Abstract

We experiment with modifications of the BSSN form of the Einstein field equations (a reformulation of the ADM equations) and demonstrate how these modifications affect the stability of numerical black hole evolution calculations. We use excision to evolve both non-rotating and rotating Kerr-Schild black holes in octant and equatorial symmetry, and without any symmetry assumptions, and obtain accurate and stable simulations for specific angular momenta J/M of up to about 0.9M.