Local Thermodynamics and Entropy for Relativistic Hydrostatic Equilibrium

TL;DR

This paper refines a method to construct entropy current and density in relativistic hydrostatic systems, demonstrating their consistency with thermodynamic laws and applying the framework to model a degenerate star.

Contribution

It introduces a non-Noether conserved charge approach to relativistic thermodynamics in Einstein gravity, ensuring non-perturbative consistency with thermodynamic laws.

Findings

Entropy density satisfies local Euler relation and first law.

Analytical expressions for thermodynamic observables in a uniform energy density system.

Framework applicable to models of degenerate stars.

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.