Energy of gravitational radiation in plane-symmetric space-times

TL;DR

This paper develops a framework for describing gravitational radiation in plane-symmetric space-times using a complex potential, deriving an energy tensor and conservation laws, and predicting a transverse pressure effect.

Contribution

It introduces a non-linear wave equation for the gravitational radiation potential and an effective energy tensor, extending previous linearized approaches.

Findings

Energy tensor reduces to Isaacson tensor in high-frequency limit

Derived an energy conservation equation for quasi-local energy

Predicted a transverse pressure exerted by low-frequency gravitational waves

Abstract

Gravitational radiation in plane-symmetric space-times can be encoded in a complex potential, satisfying a non-linear wave equation. An effective energy tensor for the radiation is given, taking a scalar-field form in terms of the potential, entering the field equations in the same way as the matter energy tensor. It reduces to the Isaacson energy tensor in the linearized, high-frequency approximation. An energy conservation equation is derived for a quasi-local energy, essentially the Hawking energy. A transverse pressure exerted by interacting low-frequency gravitational radiation is predicted.