Thermodynamics of BTZ Black Holes in Nonlinear Electrodynamics

TL;DR

This paper explores the thermodynamics and stability of charged BTZ black holes in (2+1) dimensions within nonlinear electrodynamics, revealing phase behaviors and stability conditions influenced by the cosmological constant as pressure.

Contribution

It provides a detailed thermodynamic analysis of BTZ black holes in nonlinear electrodynamics, including phase transitions and stability criteria, extending previous studies to nonlinear electromagnetic fields.

Findings

Black holes can have one or two horizons depending on parameters.

Thermodynamic quantities depend on horizon radius and temperature.

Black holes exhibit Van der Waals-like phase behavior.

Abstract

We investigate electrically charged black holes in $(2+1)$ dimensional gravity coupled to nonlinear electrodynamics (NED). The metric function $f(r)$ is depicted, showing that there can be one or two horizons. We study black hole thermodynamics in extended phase space. The cosmological constant played the role of thermodynamics pressure. Electrostatic potential, vacuum polarization, internal energy, Helmholtz and Gibbs free energies as functions of black hole horizon and Hawking temperature were analysed. The global stability of the black hole is discussed. The specific heat and local thermodynamic stability of black holes are studied. Finally, the Van der Walls behaviour of the black holes is investigated.