Noncommutative black holes in extended anti-de Sitter phase space

TL;DR

This paper explores the thermodynamics of noncommutative black holes in extended anti-de Sitter space, revealing phase transitions similar to Van der Waals fluids and novel anti-Hawking-Page transitions across different dimensions.

Contribution

It introduces the treatment of cosmological constant and minimal length as thermodynamic variables in noncommutative black holes across multiple dimensions.

Findings

Four-dimensional black holes show Van der Waals-like phase transitions.

Three-dimensional black holes are thermodynamically stable.

Two-dimensional black holes exhibit a new anti-Hawking-Page transition.

Abstract

We study thermodynamic aspects of ordinary and lower dimensional noncommutative black holes within an extended anti-de Sitter phase space by treating the negative cosmological constant and the minimal cut-off length as thermodynamic variables representing the pressure and tension of the system, respectively. In four-dimensional spacetime, the regular black hole exhibits a small/large black hole phase transition analogous to the liquid/gas transition of a Van der Waals gas. The three-dimensional case demonstrates global and local thermodynamic stability, while the two-dimensional case reveals a novel type of transition referred to as the anti-Hawking-Page transition.