A symmetry-breaking mechanism for the Z4 general-covariant evolution system

TL;DR

This paper introduces a symmetry-breaking mechanism within the Z4 formalism that unifies various hyperbolic evolution systems in Numerical Relativity, supported by stability and strong field tests.

Contribution

It proposes a novel symmetry-breaking approach that recovers known formalisms like BSSN and KST within the Z4 framework, enhancing the flexibility of evolution systems.

Findings

Successfully recovers BSSN and Bona-Massó formalisms

Encompasses the full five-parameter KST family

Demonstrates stability with noise and gravitational wave collapse tests

Abstract

The general-covariant Z4 formalism is further analyzed. The gauge conditions are generalized with a view to Numerical Relativity applications and the conditions for obtaining strongly hyperbolic evolution systems are given both at the first and the second order levels. A symmetry-breaking mechanism is proposed that allows one, when applied in a partial way, to recover previously proposed strongly hyperbolic formalisms, like the BSSN and the Bona-Mass\'o ones. When applied in its full form, the symmetry breaking mechanism allows one to recover the full five-parameter family of first order KST systems. Numerical codes based in the proposed formalisms are tested. A robust stability test is provided by evolving random noise data around Minkowski space-time. A strong field test is provided by the collapse of a periodic background of plane gravitational waves, as described by the Gowdy metric.