Gravitational radiation, energy and reaction on quasi-spherical black holes

TL;DR

This paper introduces a local energy tensor for gravitational radiation near quasi-spherical black holes, enabling analysis of radiation reaction and back-reaction effects within Einstein's equations.

Contribution

It defines a local energy tensor for gravitational waves and demonstrates its use in modeling back-reaction on quasi-spherical black holes.

Findings

Local energy tensor for gravitational radiation is covariantly conserved.

The strain for distant detectors is straightforwardly defined.

Inclusion of the energy tensor in Einstein equations models radiation reaction.

Abstract

Gravitational radiation is locally defined where the wavefronts are roughly spherical. A local energy tensor is defined for the gravitational radiation. Including this energy tensor as a source in the truncated Einstein equations describes gravitational radiation reaction, such as back-reaction on a roughly spherical black hole. The energy-momentum in a canonical frame is covariantly conserved. The strain to be measured by a distant detector is simply defined.