Null boundary phase space: slicings, news and 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.

26 pages+appendices, references added, published version in JHEP

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