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.
Highlights
The study of field theories requires the specification of fall-off or boundary conditions, which can lead to physical degrees of freedom that reside at the boundary
We are interested in maximizing the number of boundary degrees of freedom (BDOF), in the sense that for a given bulk theory there exists no consistent set of boundary conditions that leads to more BDOF than this maximal number, for a given boundary
We studied null boundary symmetries and associated D towers of charges that are functions over N
Summary
The study of field theories requires the specification of fall-off or boundary conditions, which can lead to physical degrees of freedom that reside at the boundary. We construct and study the maximal set of BDOF for a given null hypersurface This is achieved by solving the Einstein equations without imposing boundary conditions, leading to a solution space involving D(D − 3) functions over N that correspond to the bulk gravitons and D additional functions over N that specify the BDOF, in line with the analysis of [1]. In appendix D we rewrite the Kerr solution in the coordinate system adopted here and discuss its conserved charges
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