On the canonical energy of weak gravitational fields with a cosmological constant $\Lambda \in \mathbb{R}$

TL;DR

This paper investigates the canonical energy of linearized gravitational fields with a cosmological constant on various backgrounds, deriving asymptotic symmetries and a renormalized energy formula that generalizes the Trautman-Bondi mass.

Contribution

It introduces a renormalized energy definition for weak gravitational fields with a cosmological constant, applicable across different backgrounds, and connects it to asymptotic symmetries.

Findings

Energy diverges for positive cosmological constant without renormalization

A well-defined flux formula is obtained through renormalization

Renormalized energy matches a generalized Trautman-Bondi mass

Abstract

We analyse the canonical energy of vacuum linearised gravitational fields on light cones on a de Sitter, Minkowski, and Anti de Sitter backgrounds in Bondi gauge. We derive the associated asymptotic symmetries. When $\Lambda>0$ the energy diverges, but a renormalised formula with well defined flux is obtained. We show that the renormalised energy in the asymptotically off-diagonal gauge coincides with the quadratisation of the generalisation of the Trautman-Bondi mass proposed in [13].