# Thermodynamics and Phase Transition of a Nonlinear Electrodynamics Black Hole in a Cavity

## TL;DR

This paper explores the thermodynamics and phase transitions of nonlinear electrodynamics black holes in a cavity, revealing diverse phase behaviors and transitions depending on the nonlinearity strength, with implications differing from AdS boundary conditions.

## Contribution

It provides a detailed analysis of the thermodynamics and phase structure of Born-Infeld black holes in a cavity, highlighting differences from AdS boundary conditions and identifying phase transition types.

## Key findings

- Hawking-Page-like and van der Waals-like phase transitions occur in weak nonlinearity regimes.
- Only Hawking-Page-like phase transitions occur in strong nonlinearity regimes.
- A tricritical point appears in the phase diagram for weak nonlinearities.

## Abstract

We discuss the thermodynamics of a general nonlinear electrodynamics (NLED) asymptotically flat black hole enclosed in a finite spherical cavity. A canonical ensemble is considered, which means that the temperature and the charge on the wall of the cavity are fixed. After the free energy is obtained by computing the Euclidean action, it shows that the first law of thermodynamics is satisfied at the locally stationary points of the free energy. Focusing on a Born-Infeld (BI) black hole in a cavity, the phase structure and transition in various regions of the parameter space are investigated. In the region where the BI electrodynamics has weak nonlinearities, Hawking-Page-like and van der Waals-like phase transitions occur, and a tricritical point appears. In the region where the BI electrodynamics has strong enough nonlinearities, only Hawking-Page-like phase transitions occur. The phase diagram of the BI black hole in a cavity can have dissimilarity from that of a BI black hole using asymptotically anti-de Sitter boundary conditions. The dissimilarity may stem from a lack of an appropriate reference state with the same charge and temperature for the BI-AdS black hole.