Lightcone reference for total gravitational energy

TL;DR

This paper introduces a new explicit expression for gravitational energy based on physical spacetime geometry, aligning with known energy definitions in various spacetime asymptotics, derived through a lightcone reference approach.

Contribution

It presents a novel boundary-based gravitational energy expression derived from a lightcone reference, unifying different energy concepts in general relativity.

Findings

Matches ADM and Bondi energies in flat spacetimes

Aligns with Abbott-Deser energy in AdS spacetimes

Provides a boundary value of the gravitational Hamiltonian

Abstract

We give an explicit expression for gravitational energy, written solely in terms of physical spacetime geometry, which in suitable limits agrees with the total Arnowitt-Deser-Misner and Trautman-Bondi-Sachs energies for asymptotically flat spacetimes and with the Abbot-Deser energy for asymptotically anti-de Sitter spacetimes. Our expression is a boundary value of the standard gravitational Hamiltonian. Moreover, although it stands alone as such, we derive the expression by picking the zero-point of energy via a ``lightcone reference.''