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.
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Adami, H., Grumiller, D., Sheikh-Jabbari, M.M. et al. Null boundary phase space: slicings, news & memory. J. High Energ. Phys. 2021, 155 (2021). https://doi.org/10.1007/JHEP11(2021)155
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DOI: https://doi.org/10.1007/JHEP11(2021)155