Temperature for the (2+1)-dimensional Black Hole with Non Linear Electrodynamics from the Generalized Uncertainty Principle

TL;DR

This paper investigates the thermodynamics of a (2+1)-dimensional black hole with nonlinear electrodynamics using the Generalized Uncertainty Principle, revealing a minimum mass remnant and positive heat capacity.

Contribution

It introduces a novel analysis of black hole temperature and thermodynamics incorporating GUP effects in a (2+1)-dimensional setting with nonlinear electrodynamics.

Findings

Existence of a minimum black hole mass and horizon size.

Black hole heat capacity remains positive.

Presence of a black hole remnant at Planck scale.

Abstract

In this paper, we study the thermodynamical properties of the (2+1) dimensional black hole with a non-linear electrodynamics and with a negative cosmological constant, using the Generalized Uncertainty Principle (GUP). This approach shows that there is a minimum mass or remnant for the black hole, corresponding to the minimum radius of the event horizon that has a size of the order of the Planck scale. We also show that the heat capacity for this black hole is always positive.