Null boundary phase space: slicings, news & memory
2021
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.
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