Phase transitions of regular Schwarzschild-Anti-deSitter black holes

TL;DR

This paper investigates regular Schwarzschild-Anti-deSitter black holes, revealing a phase transition analogous to a van der Waals fluid, with the cosmological constant treated as a dynamic thermodynamic variable.

Contribution

It introduces a regular Schwarzschild-Anti-deSitter solution incorporating noncommutative effects and extends the Hawking-Page transition to a van der Waals-like phase diagram.

Findings

Identifies a first-order small/large black hole transition.

Extends the phase diagram to include noncommutative effects.

Treats the cosmological constant as a thermodynamic variable.

Abstract

We study a solution of the Einstein's equations generated by a self-gravitating, anisotropic, static, non-singular matter fluid. The resulting Schwarzschild like solution is regular and accounts for smearing effects of noncommutative fluctuations of the geometry. We call this solution regular Schwarzschild spacetime. In the presence of an Anti-deSitter cosmological term, the regularized metric offers an extension of the Hawking-Page transition into a van der Waals-like phase diagram. Specifically the regular Schwarzschild-Anti-deSitter geometry undergoes a first order small/large black hole transition similar to the liquid/gas transition of a real fluid. In the present analysis we have considered the cosmological constant as a dynamical quantity and its variation is included in the first law of black hole thermodynamics.