Local Thermodynamics and Entropy for Relativistic Hydrostatic Equilibrium
Abstract
By refining the method proposed in arXiv:2010.07660, entropy current and entropy density for a relativistic hydrostatic equilibrium system with spherical symmetry are constructed as a non-Noether conserved charge in the Einstein gravity with cosmological constant. It is shown that the constructed entropy density satisfies both the local Euler relation and the first law of thermodynamics non-perturbatively with respect to the Newton constant. Finally the established relativistic thermodynamics is applied to one of the systems with uniform energy density as a crude model of a degenerate star and its local thermodynamic observables are determined analytically.
Cite
@article{arxiv.2304.06196,
title = {Local Thermodynamics and Entropy for Relativistic Hydrostatic Equilibrium},
author = {Shuichi Yokoyama},
journal= {arXiv preprint arXiv:2304.06196},
year = {2024}
}
Comments
9 pages, no figure, v2: some explanations, footnotes and references added, v3: additional comparisons, comments and references added, published version