The Wald-Zoupas prescription for asymptotic charges at null infinity in general relativity

TL;DR

This paper derives explicit covariant formulas for asymptotic charges and fluxes at null infinity in vacuum general relativity, improving coordinate independence and comparison with previous methods.

Contribution

It provides covariant, local, and conformally-invariant expressions for charges and fluxes at null infinity, applicable in non-stationary regions and independent of coordinate choices.

Findings

Explicit covariant charge and flux formulas derived

Comparison with existing formulas like Ashtekar-Streubel and Komar included

Formulas are coordinate-independent and applicable in non-stationary regions

Abstract

We use the formalism developed by Wald and Zoupas to derive explicit covariant expressions for the charges and fluxes associated with the Bondi-Metzner-Sachs symmetries at null infinity in asymptotically flat spacetimes in vacuum general relativity. Our expressions hold in non-stationary regions of null infinity, are local and covariant, conformally-invariant, and are independent of the choice of foliation of null infinity and of the chosen extension of the symmetries away from null infinity. While similar expressions have appeared previously in the literature in Bondi-Sachs coordinates (to which we compare our own), such a choice of coordinates obscures these properties. Our covariant expressions can be used to obtain charge formulae in any choice of coordinates at null infinity. We also include detailed comparisons with other expressions for the charges and fluxes that have appeared in the literature: the Ashtekar-Streubel flux formula, the Komar formulae, and the linkage and twistor charge formulae. Such comparisons are easier to perform using our explicit expressions, instead of those which appear in the original work by Wald and Zoupas.