Thermodynamics of charged anti-de Sitter black holes in canonical ensemble

TL;DR

This paper explores the thermodynamics of charged anti-de Sitter black holes in the canonical ensemble, revealing potential phase transitions between non-extremal and extremal states based on action comparisons.

Contribution

It extends the thermodynamic analysis of Reissner-Nordström black holes in AdS spacetime to the canonical ensemble, highlighting conditions for phase transitions.

Findings

Non-extremal black holes generally have lower action than extremal ones.

Some small non-extremal black holes exhibit higher action, indicating possible phase transitions.

Transitions between non-extremal and extremal black holes are theoretically possible.

Abstract

As in the grand canonical treatment of Reissner - Nordstr\"{o}m black holes in anti-de Sitter spacetime, the canonical ensemble formulation also shows that non-extremal black holes tend to have lower action than extremal ones. However, some small non-extremal black holes have higher action, leading to the possibility of transitions between non-extremal and extremal black holes.