The Gravitational Radiaton degrees of freedom in Hyperbolic Systems for Numerical Relativity

TL;DR

This paper explores the gravitational radiation degrees of freedom within the 3+1 spacetime decomposition, linking them to eigenfields of the KST equations, and addresses parameter fixing related to derivative ordering ambiguities in numerical relativity.

Contribution

It establishes a connection between gravitational radiation degrees of freedom and KST eigenfields, and proposes a method to fix a parameter related to derivative ordering ambiguity.

Findings

Fixed a parameter in the KST equations related to derivative ordering.

Clarified the relationship between gravitational radiation degrees of freedom and eigenfields.

Enhanced the understanding of first order evolution systems in numerical relativity.

Abstract

The gravitational radiation degrees of freedom of freedom are described in the framework of the 3+1 decomposition of spacetime. The relationship with eigenfields of the Kidder-Scheel-Teukolsky (KST) equations is established. This relationship is used to fix a parameter in the KST equations which is related to the ordering ambiguity of space derivatives in the Ricci tensor, which is inherent to first order evolution systems, like the ones currently used in Numerical Relativity applications.