The cosmological constant and the energy of gravitational radiation

TL;DR

<3-5 sentence high-level summary> The paper develops a rigorous framework to define and analyze total mass and energy for radiating space-times with a nonzero cosmological constant Λ by extending the Bondi–Trautman program to characteristic (null) hypersurfaces. It establishes Bondi-type coordinates and Fefferman–Graham expansions to derive asymptotic metric data, and proves a mass-balance identity that involves a renormalized volume of the null hypersurface, generalizing positivity results known for Λ=0. The results connect the new characteristic mass to coordinate and Hamiltonian masses in explicit examples (Birmingham and Horowitz–Myers metrics), and provide a detailed analysis of the Λ<0 case, including the role of the boundary geometry and the no-logs conditions. Together, these findings unify several mass notions in AdS-like settings and offer a robust tool for understanding energy in radiating spacetimes with Λ ≠ 0.

Abstract

We propose a definition of mass for characteristic hypersurfaces in asymptotically vacuum space-times with non-vanishing cosmological constant $Λ\in {\mathbb R}^*$, generalising the definition of Trautman and Bondi for $Λ=0$. 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 $Λ=0$.

Figures (1)

• Figure 1.1: Globally smooth light-cones in space-times with a smooth conformal completion at a conformal boundary ${\mycal I}$ at timelike infinity ($\Lambda >0$, left) or spacelike infinity ($\Lambda <0$, right).