# Critical Phenomena of Born-Infeld-de Sitter Black Holes in Cavities

## TL;DR

This paper explores the thermodynamics of Born-Infeld-de Sitter black holes in cavities, revealing unique reentrant phase transitions caused by non-linear electromagnetic effects, with implications for black hole phase structure.

## Contribution

It introduces the study of black hole thermodynamics with Born-Infeld non-linear electrodynamics in a cavity, highlighting new reentrant phase transitions not seen with standard Maxwell fields.

## Key findings

- Reentrant phase transitions occur in the canonical ensemble due to Born-Infeld non-linearities.
- A new reentrant transition from radiation to black hole and back to radiation is found in the grand canonical ensemble.
- The phase structure depends on the maximal electric field strength of the Born-Infeld theory.

## Abstract

We examine the thermodynamic behaviour of charged, asymptotically de Sitter black holes embedded in a finite-radius isothermal cavity, with a Born-Infeld gauge field replacing the ordinary Maxwell field. We find that the non-linearities of Born-Infeld theory lead to the presence of reentrant phase transitions in the canonical ensemble, whose existence and character are determined by the maximal electric field strength of the theory. We also examine the phase structure in the grand canonical ensemble, and demonstrate the presence of a new reentrant phase transition from radiation, to an intermediate size black hole, and back to radiation.