Horizon Thermodynamics from Einstein's Equation of State

TL;DR

This paper derives a comprehensive horizon first law from Einstein's equations viewed as an equation of state, generalizing to higher curvature gravities and enabling consistent black hole thermodynamics without conserved charges.

Contribution

It introduces a full cohomogeneity horizon first law from Einstein's equations as an equation of state, extending horizon thermodynamics beyond standard formulations.

Findings

Derivation of a full horizon first law from Einstein's equations.

Generalization to higher curvature gravity theories.

Establishment of a framework for black hole thermodynamics without conserved charges.

Abstract

By regarding the Einstein equations as equation(s) of state, we demonstrate that a full cohomogeneity horizon first law can be derived in horizon thermodynamics. In this approach both the entropy and the free energy are derived concepts, while the standard (degenerate) horizon first law is recovered by a Legendre projection from the more general one we derive. These results readily generalize to higher curvature gravities and establish a way of how to formulate consistent black hole thermodynamics without conserved charges.