Symmetries and charges of general relativity at null boundaries

TL;DR

This paper investigates the symmetries and charges of general relativity at null boundaries using covariant phase space formalism, revealing supertranslations' role at all null boundaries and their potential link to black hole information paradox.

Contribution

It extends the analysis of null boundary symmetries to non-stationary surfaces and derives associated charges and fluxes in a covariant manner, unifying horizon and null infinity symmetries.

Findings

Supertranslations form a nonabelian algebra at null boundaries.

Localized charges and fluxes are derived for non-stationary null surfaces.

Global charges at horizons obey the same algebra as linearized diffeomorphisms.

Abstract

We study general relativity at a null boundary using the covariant phase space formalism. We define a covariant phase space and compute the algebra of symmetries at the null boundary by considering the boundary-preserving diffeomorphisms that preserve this phase space. This algebra is the semi-direct sum of diffeomorphisms on the two sphere and a nonabelian algebra of supertranslations that has some similarities to supertranslations at null infinity. By using the general prescription developed by Wald and Zoupas, we derive the localized charges of this algebra at cross sections of the null surface as well as the associated fluxes. Our analysis is covariant and applies to general non-stationary null surfaces. We also derive the global charges that generate the symmetries for event horizons, and show that these obey the same algebra as the linearized diffeomorphisms, without any central extension. Our results show that supertranslations play an important role not just at null infinity but at all null boundaries, including non-stationary event horizons. They should facilitate further investigations of whether horizon symmetries and conservation laws in black hole spacetimes play a role in the information loss problem, as suggested by Hawking, Perry, and Strominger.