  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.
