Null boundary phase space: slicings, news & memory

Abstract

Abstract We construct the boundary phase space in D-dimensional Einstein gravity with a generic given co-dimension one null surface N $$ \mathcal{N} $$ as the boundary. The associated boundary symmetry algebra is a semi-direct sum of diffeomorphisms of N $$ \mathcal{N} $$ and Weyl rescalings. It is generated by D towers of surface charges that are generic functions over N $$ \mathcal{N} $$ . These surface charges can be rendered integrable for appropriate slicings of the phase space, provided there is no graviton flux through N $$ \mathcal{N} $$ . In one particular slicing of this type, the charge algebra is the direct sum of the Heisenberg algebra and diffeomorphisms of the transverse space, N $$ \mathcal{N} $$ v for any fixed value of the advanced time v. Finally, we introduce null surface expansion- and spin-memories, and discuss associated memory effects that encode the passage of gravitational waves through N $$ \mathcal{N} $$ , imprinted in a change of the surface charges.

Keywords

• Black Holes
• Space-Time Symmetries
• Gauge Symmetry
• Global Symmetries