Gauge Invariant Effective Stress-Energy Tensors for Gravitational Waves

TL;DR

This paper introduces a generalized gauge invariance framework allowing the definition of gauge invariant effective stress-energy tensors for gravitational waves in broader contexts, removing previous limitations on averaging and frequency restrictions.

Contribution

It presents a new approach to gauge invariance that broadens the applicability of stress-energy tensors for gravitational waves beyond high-frequency and large-scale averaging constraints.

Findings

Gauge invariant tensors can be defined without averaging over large spacetime regions.

The approach applies to gravitational waves of arbitrary frequency.

It extends the theoretical foundation for analyzing gravitational wave energy content.

Abstract

It is shown that if a generalized definition of gauge invariance is used, gauge invariant effective stress-energy tensors for gravitational waves and other gravitational perturbations can be defined in a much larger variety of circumstances than has previously been possible. In particular it is no longer necessary to average the stress-energy tensor over a region of spacetime which is larger in scale than the wavelengths of the waves and it is no longer necessary to restrict attention to high frequency gravitational waves.