Abstract
We perform a detailed study of the covariance properties of the symplectic potential of general relativity on a null hypersurface, and of the different polarizations that can be used to study conservative as well as leaky boundary conditions. This allows us to identify a one-parameter family of covariant symplectic potentials. We compute the charges and fluxes for the most general phase space with arbitrary variations. We study five symmetry groups that arise when different restrictions on the variations are included. Requiring stationarity as in the original Wald-Zoupas prescription selects a unique member of the family of symplectic potentials, the one of Chandrasekaran, Flanagan and Prabhu. The associated charges are all conserved on non-expanding horizons, but not on flat spacetime. We show that it is possible to require a weaker notion of stationarity which selects another symplectic potential, again in a unique way, and whose charges are conserved on both non-expanding horizons and flat light-cones. Furthermore, the flux of future-pointing diffeomorphisms at leading-order around an outgoing flat light-cone is positive and reproduces a tidal heating plus a memory term. We also study the conformal conservative boundary conditions suggested by the alternative polarization and identify under which conditions they define a non-ambiguous variational principle. Our results have applications for dynamical notions of entropy, and are useful to clarify the interplay between different boundary conditions, charge prescriptions, and symmetry groups that can be associated with a null boundary.
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Acknowledgments
We thank Alejandro Perez and Antony Speranza for many discussions on the topics of this paper, and Venkatesa Chandrasekaran and Eanna Flanagan for discussions and exchanges on our drafts. We acknowledge support from the John Templeton Foundation via the grant n.62312, as part of the project The Quantum Information Structure of Spacetime (QISS). The opinions expressed in this publication are those of the author and do not necessarily reflect the views of the John Templeton Foundation.
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Odak, G., Rignon-Bret, A. & Speziale, S. General gravitational charges on null hypersurfaces. J. High Energ. Phys. 2023, 38 (2023). https://doi.org/10.1007/JHEP12(2023)038
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DOI: https://doi.org/10.1007/JHEP12(2023)038