Null boundary phase space: slicings, news & memory

Abstract

We construct the boundary phase space in D-dimensional Einstein gravity with a generic given co-dimension one null surface $\mathcal{N}$ as the boundary. The associated boundary symmetry algebra is a semi-direct sum of diffeomorphisms of $\mathcal{N}$ and Weyl rescalings. It is generated by D towers of surface charges that are generic functions over $\mathcal{N}$. These surface charges can be rendered integrable for appropriate slicings of the phase space, provided there is no graviton flux through $\mathcal{N}$. In one particular slicing of this type, the charge algebra is the direct sum of the Heisenberg algebra and diffeomorphisms of the transverse space, $\mathcal{N}$_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 $\mathcal{N}$, imprinted in a change of the surface charges.