Black hole entropy and Lorentz-diffeomorphism Noether charge

TL;DR

This paper demonstrates that black hole entropy can be derived as a horizon Noether charge associated with combined diffeomorphism and Lorentz symmetries in the frame formalism, applicable to various gravity theories.

Contribution

It introduces a novel approach to calculating black hole entropy using a combined symmetry Noether charge in the frame formalism, extending to multiple gravity models.

Findings

Black hole entropy corresponds to a horizon Noether charge involving Lorentz-diffeomorphism symmetry.

Diffeomorphism-only Noether charge is inadequate due to frame invariance issues.

Applicable to general relativity, Lovelock gravity, and topological terms.

Abstract

We show that, in the first or second order orthonormal frame formalism, black hole entropy is the horizon Noether charge for a combination of diffeomorphism and local Lorentz symmetry involving the Lie derivative of the frame. The Noether charge for diffeomorphisms alone is unsuitable, since a regular frame cannot be invariant under the flow of the Killing field at the bifurcation surface. We apply this formalism to Lagrangians polynomial in wedge products of the frame field 1-form and curvature 2-form, including general relativity, Lovelock gravity, and "topological" terms in four dimensions.