Thermodynamics of the (2+1)-dimensional Black Hole with non linear Electrodynamics and without Cosmological Constant from the Generalized Uncertainly Principle

TL;DR

This paper investigates the thermodynamics of a (2+1)-dimensional black hole influenced by non-linear electrodynamics without a cosmological constant, using the Generalized Uncertainty Principle, revealing a maximum temperature and typical heat capacity behavior.

Contribution

It introduces a novel analysis of black hole thermodynamics incorporating GUP effects in a non-linear electrodynamics context without cosmological constant.

Findings

Existence of a maximum temperature depending on electric charge.

Black hole heat capacity exhibits expected thermodynamic behavior.

Minimum event horizon radius is of the order of the Planck scale.

Abstract

In this paper, we study the thermodynamical properties of the (2+1)dimensional black hole with a non-linear electrodynamics and without cosmological constant using the Generalized Uncertainty Principle (GUP). This approach shows that there is a maximum temperature for the black hole depending only on the electric charge and corresponding to the minimum radius of the event horizon, of the order of the Planck scale. Finally we show that the heat capacity for this black hole has the expected behavior.