Spatially local energy density of gravitational waves

TL;DR

This paper introduces a new set of BMS charges at null infinity, enabling the definition of a spatially localized energy density of gravitational waves that can be measured through local experiments over time.

Contribution

It develops a unique, covariant set of BMS charges with a super-translation flux containing only the hard term, and uses them to define a measurable local energy density of gravitational waves.

Findings

New BMS charges with super-translation flux only containing the hard term.

A covariant, center-less realization of the symmetry algebra.

A method to measure gravitational wave energy density locally.

Abstract

We propose a new set of BMS charges at null infinity, characterized by a super-translation flux that contains only the `hard' term. This is achieved with a specific corner improvement of the symplectic 2-form, and we spell the conditions under which it is unique. The charges are associated to a Wald-Zoupas symplectic potential, and satisfy all standard criteria: they are covariant, provide a center-less realization of the symmetry algebra, have vanishing flux in non-radiative spacetimes, and vanish in Minkowski. We use them to define a notion of spatially localized energy density of gravitational waves, and explain how it can be measured doing experiments which are purely local in space and over an extended period of time.