Near-Horizon Symmetries in Einstein-Maxwell theory

TL;DR

This work addresses near-horizon symmetries in four-dimensional Einstein–Maxwell theory by employing the covariant phase space formalism to derive horizon charges and fluxes. It solves the near-horizon geometry using a radial expansion of the metric and Maxwell field in the Newman–Unti gauge, yielding explicit expressions for the horizon data and their evolution. The authors compute canonical and EM charges for horizon diffeomorphisms, reveal that the Carrollian internal boost corresponds to a Lorentz boost and identify a corner-area charge as a gravitational entropy proxy, with the charge algebra closing under the generalized Barnich–Troessaert bracket. They show that the flux-balance law reproduces the Damour and Raychaudhuri equations on the horizon and discuss implications for horizon thermodynamics and entropy, while outlining open questions about extending to spacelike sectors and potential spin-2 symmetries.

Abstract

This manuscript aims to provide a comprehensive derivation of the Einstein-Maxwell charges and fluxes in the near-horizon region of a four-dimensional non-extremal black hole, with vanishing cosmological constant. Specifically, we present a detailed derivation of the Noether charges within both the metric and first-order formulations, elucidating the relationship between the Carrollian internal boost charge and the Lorentz boost charge. It is well-established in the literature that Carrollian fluids exhibit an internal local boost symmetry; we demonstrate that this symmetry precisely corresponds to a Lorentz internal transformation. Finally, we prove that the near-horizon Einstein equations can be obtained from the flux-balance law by employing the generalized Barnich-Troessaert bracket.