Conservation of asymptotic charges from past to future null infinity: Lorentz charges in general relativity

TL;DR

This paper proves that Lorentz and BMS asymptotic charges in certain asymptotically-flat spacetimes are conserved and match across past, future, and spatial infinities, confirming a conjecture by Strominger.

Contribution

It demonstrates the matching and conservation of all BMS charges across null and spatial infinities in a specific class of spacetimes, extending previous results.

Findings

Lorentz charges match at null and spatial infinity.

All BMS charges are conserved in classical gravitational scattering.

The results confirm Strominger's conjecture on charge matching.

Abstract

We show that the asymptotic charges associated with Lorentz symmetries on past and future null infinity match in the limit to spatial infinity in a class of asymptotically-flat spacetimes. These are spacetimes that obey the Ashtekar-Hansen definition of asymptotic flatness at null and spatial infinity and satisfy an additional set of conditions which we lay out explicitly. Combined with earlier results on the matching of supertranslation charges, this shows that all Bondi-Metzner-Sachs (BMS) charges on past and future null infinity match in the limit to spatial infinity in this class of spacetimes, proving a relationship that was conjectured by Strominger. Assuming additional suitable conditions are satisfied at timelike infinities, this proves that the flux of all BMS charges is conserved in any classical gravitational scattering process in these spacetimes.