Gauge Invariant Derivation of Zeroth and First Laws of Black Hole Thermodynamics

TL;DR

This paper presents a gauge invariant derivation of the zeroth and first laws of black hole thermodynamics, ensuring that all physical quantities involved are gauge invariant, which clarifies their fundamental nature.

Contribution

It introduces a gauge invariant approach to derive and prove the zeroth and first laws of black hole thermodynamics, addressing previous subtleties in gauge invariance.

Findings

Gauge invariance of thermodynamic quantities is established.

A consistent derivation of black hole thermodynamics laws is provided.

Clarifies the role of gauge invariance in black hole physics.

Abstract

In gauge invariant theories, like Einstein-Maxwell theory, physical observables should be gauge invariant. In particular, mass, entropy, angular momentum, electric charge and their respective chemical potentials, temperature, horizon angular velocity and electric potential which appear in the laws of black hole thermodynamics should be gauge invariant. In the usual construction of the laws of black hole thermodynamics, gauge invariance of the intensive quantities is subtle; here we remedy this and provide a gauge invariant derivation and the proof of the zeroth and first laws of black hole thermodynamics.