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.
Versions
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BibTeX
@misc{koivisto2026hamiltonian,
title = {{Hamiltonian surface charges in General Parallel Relativity}},
author = {Tomi Koivisto},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16799},
eprint = {2610.16799},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16799},
}
RIS
TY - UNPB
TI - Hamiltonian surface charges in General Parallel Relativity
AU - Tomi Koivisto
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16799
UR - https://arxiv.org/abs/2610.16799
AB - 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.
ER -