On the Energy-Momentum Density of Gravitational Plane Waves

TL;DR

This paper develops a covariant, variational framework for gravitational stress-energy, constructs a tensor analogous to electromagnetic stress-energy, and identifies energy-momentum in gravitational plane waves.

Contribution

It introduces a new covariant tensor for gravitational energy-momentum derived from a variational principle, extending Einstein's formulation.

Findings

A tensor $T^G$ is constructed from the Bel tensor and a symmetric tensor field.

Helicity-2 polarized gravitational waves carry non-zero energy and momentum.

The framework aligns gravitational stress-energy with electromagnetic analogs.

Abstract

By embedding Einstein's original formulation of GR into a broader context we show that a dynamic covariant description of gravitational stress-energy emerges naturally from a variational principle. A tensor $T^G$ is constructed from a contraction of the Bel tensor with a symmetric covariant second degree tensor field $\Phi$ and has a form analogous to the stress-energy tensor of the Maxwell field in an arbitrary space-time. For plane-fronted gravitational waves helicity-2 polarised (graviton) states can be identified carrying non-zero energy and momentum.