Consistency between dynamical and thermodynamical stabilities for charged self-gravitating perfect fluid

TL;DR

This paper demonstrates that for charged self-gravitating perfect fluids, the dynamical and thermodynamical stability criteria are equivalent, extending the connection between gravity and thermodynamics to include electromagnetic effects.

Contribution

It recasts the stability criteria for charged fluids in Einstein-Maxwell theory and proves their equivalence, highlighting the thermodynamic-gravitational link with electric fields.

Findings

Dynamical and thermodynamical stability criteria are equivalent for charged fluids.

General formula for the second variation of total entropy in charged cases.

Thermodynamical stability criterion derived for radial perturbations.

Abstract

The entropy principle shows that, for self-gravitating perfect fluid, the Einstein field equations can be derived from the extrema of the total entropy, and the thermodynamical stability criterion are equivalent to the dynamical stability criterion. In this paper, we recast the dynamical criterion for the charged self-gravitating perfect fluid in Einstein-Maxwell theory, and further give the criterion of the star with barotropic condition. In order to obtain the thermodynamical stability criterion, first we get the general formula of the second variation of the total entropy for charged perfect fluid case, and then obtain the thermodynamical criterion for radial perturbation. We show that these two stability criterion are the same, which suggest that the inherent connection between gravity and thermodynamic even when the electric field is taken into account.