The cosmological constant and the energy of gravitational radiation

TL;DR

This paper introduces a new definition of mass for characteristic hypersurfaces in asymptotically vacuum space-times with a non-zero cosmological constant, extending previous concepts and establishing a balance formula.

Contribution

It generalizes the Trautman-Bondi mass to cases with non-zero cosmological constant and proves a related balance formula linking mass and volume.

Findings

The new mass definition reduces to standard definitions in special cases.

A balance formula relating mass and volume is established.

The approach extends positivity identities to non-zero cosmological constant scenarios.

Abstract

We propose a definition of mass for characteristic hypersurfaces in asymptotically vacuum space-times with non-vanishing cosmological constant $\Lambda \in {\mathbb R}^*$, generalising the definition of Trautman and Bondi for $\Lambda=0$. We show that our definition reduces to some standard definitions in several situations. We establish a balance formula linking the characteristic mass and a suitably defined renormalised volume of the null hypersurface, generalising the positivity identity of one of us (PTC) and Paetz proved when $\Lambda=0$.