Explicit Gravitational Radiation in Hyperbolic Systems for Numerical Relativity

TL;DR

This paper introduces a geometric method for analyzing hyperbolic evolution systems in numerical relativity, explicitly identifying gravitational radiation degrees of freedom in a covariant manner, and providing a benchmark for future formalisms.

Contribution

It presents a covariant, geometrically motivated approach to characterize gravitational radiation in hyperbolic systems, resolving ordering ambiguities in first order formulations.

Findings

Intrinsic identification of gravitational wave degrees of freedom

A covariant interpretation linked to wave front geometry

A benchmark for testing hyperbolic formalisms in numerical relativity

Abstract

A method for studying the causal structure of space-time evolution systems is presented. This method, based on a generalization of the well known Riemann problem, provides intrinsic results which can be interpreted from the geometrical point of view. A one-parameter family of hyperbolic evolution systems is presented and the physical relevance of their characteristic speeds and eigenfields is discussed. The two degrees of freedom corresponding to gravitational radiation are identified in an intrinsic way, independent of the space coordinate system. A covariant interpretation of these degrees of freedom is provided in terms of the geometry of the wave fronts. The requirement of a consistent geometrical interpretation of the gravitational radiation degrees of freedom is used to solve the ordering ambiguity that arises when obtaining first order evolution systems from the second order field equations. This achievement provides a benchmark which can be used to check both the existing and future first order hyperbolic formalisms for Numerical Relativity.