A Radiation Scalar for Numerical Relativity

TL;DR

This paper introduces a new scalar curvature invariant in general relativity that identifies regions with gravitational radiation and provides a coordinate-independent way to analyze such radiation locally.

Contribution

It presents a novel scalar curvature invariant that vanishes outside gravitational radiation zones and can be extended smoothly to general space-time regions.

Findings

Invariant vanishes in non-radiative regions

Can extract local radiation information

Smooth extension to generic space-time regions

Abstract

This letter describes a scalar curvature invariant for general relativity with a certain, distinctive feature. While many such invariants exist, this one vanishes in regions of space-time which can be said unambiguously to contain no gravitational radiation. In more general regions which incontrovertibly support non-trivial radiation fields, it can be used to extract local, coordinate-independent information partially characterizing that radiation. While a clear, physical interpretation is possible only in such radiation zones, a simple algorithm can be given to extend the definition smoothly to generic regions of space-time.