On Thermodynamic Stability of Black Holes. Part I: Classical Stability

TL;DR

This paper systematically applies classical thermodynamic criteria to analyze the stability of black holes, emphasizing the importance of complete conditions and heat capacities, and exploring phase transitions and limits in classical black hole thermodynamics.

Contribution

It introduces a comprehensive framework for assessing black hole thermodynamic stability using classical criteria, highlighting potential pitfalls of incomplete analyses.

Findings

Identified the importance of full heat capacity analysis for stability

Mapped critical points and phase transition curves

Clarified limits of classical thermodynamic analysis for black holes

Abstract

We revisit the classical thermodynamic stability of the standard black hole solutions by implementing the intrinsic necessary and sufficient conditions for stable global and local thermodynamic equilibrium. The criteria for such equilibria are quite generic and well-established in classical thermodynamics, but they have not been fully utilized in black hole physics. We show how weaker or incomplete conditions could lead to misleading or incorrect results for the thermodynamic stability of the system. We also stress the importance of finding all possible local heat capacities in order to fully describe the classical equilibrium picture of black holes. Finally, we thoroughly investigate the critical and phase transition curves and the limits of the classical analysis. This paper is the first in the line of intended works on thermodynamic stability of black holes in modified theories of gravity and holography.