On the energy of gravitational waves

TL;DR

This paper proposes a new quasilocal approach to defining the energy of gravitational waves, addressing limitations of previous methods and aligning with the principle that gravitational energy can only be defined locally via closed surfaces.

Contribution

A novel method to derive gravitational wave energy directly from quasilocal gravitational energy, improving upon existing descriptions like Isaacson's tensor.

Findings

Addresses defects in previous energy definitions

Provides a consistent quasilocal energy framework

Enhances understanding of gravitational wave energetics

Abstract

The energy of gravitational waves is a fundamental problem in gravity theory. The existing descriptions for the energy of gravitational waves, such as the well-known Isaacson energy-momentum tensor, suffer from several defects. Due to the equivalence principle, the gravitational energy-momentum can only be defined quasilocally, being associated with a closed spacelike 2-surface bounding a region. We propose a new approach to derive the energy of gravitational waves $directly$ from the quasilocal gravitational energy. Such an approach is natural and consistent with the quasilocality of gravitational energy-momentum.