Gauge invariant derivation of zeroth and first laws of black hole thermodynamics

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