Hamiltonian surface charges in General Parallel Relativity

Abstract

General Parallel Relativity is a dynamically equivalent formulation of Einstein gravity in which the parallel frame supplies explicit boundary reference data. In this formulation, finite-region energy-momentum and horizon entropy arise as distinct Hamiltonian surface charges. Diffeomorphisms along canonical frame directions define a quasi-local energy-momentum including a matter surface term, while normal-plane boosts at a smooth horizon give entropy. These covariant formulas are applied to the Reissner-Nordström black hole and to a dilatonic charged black hole. In both examples, the matter contribution and its Legendre transform complete the Misner-Sharp mass into the Hamiltonian energy appropriate to the chosen electromagnetic boundary datum. The resulting horizon charges satisfy the thermodynamic relation obtained independently from the Euclidean boundary action.