Regular black holes in isothermal cavity

TL;DR

This paper investigates the thermodynamics and phase transitions of regular black holes within an isothermal cavity, revealing a novel small/large black hole transition analogous to a Van der Waals fluid.

Contribution

It derives a new reduced action incorporating quantum corrections for regular black holes in a cavity and analyzes their phase structure, highlighting a unique black hole transition.

Findings

Identifies a stable small/large black hole phase transition in a cavity.

Shows the transition resembles a Van der Waals liquid/gas phase change.

Demonstrates quantum corrections influence black hole thermodynamics.

Abstract

We examine the thermodynamic behavior of a static neutral regular (non-singular) black hole enclosed in a finite isothermal cavity. The cavity enclosure helps us investigate black hole systems in a canonical or a grand canonical ensemble. Here we demonstrate the derivation of the reduced action for the general metric of a regular black hole in a cavity by considering a canonical ensemble. The new expression of the action contains quantum corrections at short distances and concludes to the action of a singular black hole in a cavity at large distances. We apply this formalism to the noncommutative Schwarzschild black hole, in order to study the phase structure of the system. We conclude to a possible small/large stable regular black hole transition inside the cavity that exists neither at the system of a classical Schwarzschild black hole in a cavity, nor at the asymptotically flat regular black hole without the cavity. This phase transition seems to be similar with the liquid/gas transition of a Van der Waals gas.