Extending the lifetime of 3D black hole computations with a new hyperbolic system of evolution equations

TL;DR

This paper introduces a new family of hyperbolic evolution equations for Einstein's equations, demonstrating improved stability in 3D black hole simulations and extending the simulation lifetime significantly.

Contribution

The authors develop a generalized hyperbolic system of Einstein's equations and show its effectiveness in stable, long-term 3D black hole evolutions.

Findings

Stable evolution for up to 1300 M in single black hole simulations

Simulation stability depends on hyperbolic system parameters

Potential applicability to binary black hole evolutions

Abstract

We present a new many-parameter family of hyperbolic representations of Einstein's equations, which we obtain by a straightforward generalization of previously known systems. We solve the resulting evolution equations numerically for a Schwarzschild black hole in three spatial dimensions, and find that the stability of the simulation is strongly dependent on the form of the equations (i.e. the choice of parameters of the hyperbolic system), independent of the numerics. For an appropriate range of parameters we can evolve a single 3D black hole to $t \simeq 600 M$ -- $1300 M$, and are apparently limited by constraint-violating solutions of the evolution equations. We expect that our method should result in comparable times for evolutions of a binary black hole system.