Black hole thermodynamics is gauge independent

TL;DR

This paper demonstrates that black hole thermodynamics' first law remains gauge independent in the first-order formalism, using principal fiber bundles and an alternative method to clarify its fundamental nature.

Contribution

It introduces a new approach that directly proves gauge independence of the first law, simplifying calculations and resolving ambiguities in black hole thermodynamics.

Findings

First law is gauge independent in the first-order formalism.

New method simplifies computations of black hole thermodynamics.

Clarifies ambiguities in gauge choice and thermodynamic analysis.

Abstract

Black hole thermodynamics provides a rare window into the elusive quantum nature of gravity. In the first-order formalism for gravitational theories, where torsion and gauge freedom are present, it has been suggested that the first law of black hole thermodynamics requires a specific gauge choice, which would undermine its fundamental character. By using principal fiber bundles, it has been shown that the first law is independent of this gauge choice. The present work introduces an alternative method that establishes this independence in a more direct manner, thereby reinforcing the status of the first law as a guide toward quantum gravity. This method also facilitates explicit computations of the first law and helps resolve several ambiguities that commonly appear in such analyses.