Corrigendum to "Thermodynamical instabilities of perfect fluid spheres in General Relativity"

TL;DR

This corrigendum clarifies and corrects previous results on the thermodynamic stability of perfect fluid spheres in General Relativity, emphasizing the ensemble context and conditions for stability equivalence.

Contribution

It clarifies previous findings and corrects the ensemble interpretation of stability conditions in the study of perfect fluid spheres in General Relativity.

Findings

Clarification of thermodynamic stability conditions

Correction of ensemble interpretation from canonical to microcanonical

Specification of cases where dynamical and thermodynamic stability coincide

Abstract

In [1], the thermal equilibrium of static, spherically symmetric perfect fluids in General Relativity was studied. I would like to elaborate three points relevant to the results of [1]. The first point is only a clarification, summarized in theorem 1 below, of results that appear in [1]. The following two points correct the error in [1], stating that the condition for thermodynamic stability, found in [1], is referring to the microcanonical ensemble, while it was referring to the canonical one. In theorems 2 and 3, specific cases for which equivalence of dynamical and thermodynamic stability holds are specified.