Dynamical shift conditions for the Z4 and BSSN hyperbolic formalisms

TL;DR

This paper introduces a class of dynamical shift conditions that ensure strong hyperbolicity in Z4 and BSSN formalisms, generalizing harmonic and minimal distortion conditions for improved numerical relativity simulations.

Contribution

It identifies a new class of shift conditions that guarantee strong hyperbolicity in key formalisms, extending previous harmonic and minimal distortion approaches.

Findings

The class generalizes harmonic shift conditions.

It ensures strong hyperbolicity in Z4 and BSSN formalisms.

Connections to 'dynamical freezing' shift conditions are discussed.

Abstract

A class of dynamical shift conditions is shown to lead to a strongly hyperbolic evolution system, both in the Z4 and in the BSSN Numerical Relativity formalisms. This class generalizes the harmonic shift condition, where light speed is the only non-trivial characteristic speed, and it is contained into the multi-parameter family of minimal distortion shift conditions recently proposed by Lindblom and Scheel. The relationship with the analogous 'dynamical freezing' shift conditions used in black hole simulations discussed.