Stationarity of Extremum Entropy Fluid Bodies in General Relativity

TL;DR

This paper proves that in general relativity, perfect fluid stars that extremize entropy under fixed mass, angular momentum, and particle number are necessarily stationary with circular flow, linking thermodynamic and dynamic equilibrium.

Contribution

It demonstrates that thermodynamic extremum conditions in relativistic fluid bodies imply their stationarity and circular flow, establishing a fundamental connection between thermodynamics and dynamics.

Findings

Extremizing entropy at fixed conserved quantities leads to stationary configurations.

Such configurations exhibit circular flow patterns.

Thermodynamic equilibrium implies dynamic equilibrium in relativistic fluid stars.

Abstract

We consider perfect fluid bodies ("stars") in general relativity that are axisymmetric, asymptotically flat, and that admit a maximal hypersurface. We show that configurations that extremize the total entropy at fixed ADM mass, ADM angular momentum, and total particle number are stationary with circular flow. For such stars, this establishes that thermodynamic equilibrium implies dynamic equilibrium.