Symmetries and charges of general relativity at null boundaries
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 boundarypreserving diffeomorphisms that preserve this phase space. This algebra is the semidirect 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 nonstationary 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 nonstationary 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.
 Publication:

Journal of High Energy Physics
 Pub Date:
 November 2018
 DOI:
 10.1007/JHEP11(2018)125
 arXiv:
 arXiv:1807.11499
 Bibcode:
 2018JHEP...11..125C
 Keywords:

 Black Holes;
 Classical Theories of Gravity;
 SpaceTime Symmetries;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 v2: added appendices on trivial diffeomorphisms and relation to 1810.01847