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.

• Received 14 September 2022
• Accepted 21 October 2022

DOI:https://doi.org/10.1103/PhysRevD.106.104030

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Published by the American Physical Society