Another proof of the positive energy theorem in gravity

Abstract

We show that gravitational energy expression simplifies when a new set of coordinates that satisfies a certain asymptotic gauge condition is used. Compared to the ADM formula, positivity of the energy is more transparent in this new construction. Our proof relies on the asymptotic symmetries (specifically supertranslations) of the asymptotically flat spacetimes at spatial infinity in four dimensions.

v2: 7 pages, no figures, REVTeX4; Major revision including the change in the title, the focus is now only on the D=4 case