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Paper IPM / Physic / 17066  


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