A 3+1 covariant suite of Numerical Relativity Evolution Systems

TL;DR

This paper introduces a new set of three covariant evolution systems in 3+1 numerical relativity, demonstrating their causal structures and relationships, with potential benefits for stability and clarity in simulations.

Contribution

It presents a novel covariant suite of evolution systems in 3+1 formalism, explicitly relating parameters to characteristic speeds and maintaining tensorial behavior of variables.

Findings

The first system matches BSSN causal structure.

The second system aligns with Bona-Masso system.

The third system reduces variables to trivial modes.

Abstract

A suite of three evolution systems is presented in the framework of the 3+1 formalism. The first one is of second order in space derivatives and has the same causal structure of the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) system for a suitable choice of parameters. The second one is the standard first order version of the first one and has the same causal structure of the Bona-Masso system for a given parameter choice. The third one is obtained from the second one by reducing the space of variables in such a way that the only modes that propagate with zero characteristic speed are the trivial ones. This last system has the same structure of the ones recently presented by Kidder, Scheel and Teukolski: the correspondence between both sets of parameters is explicitly given. The fact that the suite started with a system in which all the dynamical variables behave as tensors (contrary to what happens with BSSN system) allows one to keep the same parametrization when passing from one system to the next in the suite. The direct relationship between each parameter and a particular characteristic speed, which is quite evident in the second and the third systems, is a direct consequence of the manifest 3+1 covariance of the approach.