Thermodynamics and thermal stability of BTZ-ModMax black holes

TL;DR

This paper derives an exact BTZ black hole solution within a new nonlinear electrodynamics framework, analyzing its thermodynamic properties and stability to understand its physical behavior.

Contribution

It introduces a novel BTZ black hole solution in the context of ModMax nonlinear electrodynamics and explores its thermodynamic stability.

Findings

The black hole solution exhibits specific thermodynamic characteristics.

The stability analysis identifies regions of local and global stability.

The solution satisfies the first law of thermodynamics.

Abstract

Motivated by a new interesting nonlinear electrodynamics (NLED) model which is known as Modification Maxwell (ModMax) theory, we obtain an exact analytic BTZ black hole solution in the presence of a new NLED model and the cosmological constant. Then, by considering the obtained solution, we obtain Hawking temperature, entropy, electric charge, mass, and electric potential. We extract the first law of thermodynamics for the BTZ-ModMax black hole. We study thermal stability by evaluating the heat capacity (local stability) and Helmholtz free energy (global stability). By comparing the local and global stabilities, we find the common areas that satisfy the local and global stabilities, simultaneously.