Geometrical method for thermal instability of nonlinearly charged BTZ Black Holes

TL;DR

This paper investigates the thermal stability and phase transitions of three-dimensional BTZ black holes with nonlinear electrodynamics, employing a new geometric method that successfully correlates with heat capacity analysis.

Contribution

It introduces a new geometric approach to thermodynamics of BTZ black holes that accurately identifies phase transitions, improving upon previous metrics.

Findings

Maxwell, logarithmic, and exponential theories show only type one phase transitions.

Correction form of nonlinear electrodynamics exhibits two roots and one divergence point in heat capacity.

The new geometric metric aligns with phase transition points, unlike previous metrics.

Abstract

In this paper we consider three dimensional BTZ black holes with three models of nonlinear electrodynamics as source. Calculating heat capacity, we study the stability and phase transitions of these black holes. We show that Maxwell, logarithmic and exponential theories yield only type one phase transition which is related to the root(s) of heat capacity. Whereas for correction form of nonlinear electrodynamics, heat capacity contains two roots and one divergence point. Next, we use geometrical approach for studying classical thermodynamical behavior of the system. We show that Weinhold and Ruppeiner metrics fail to provide fruitful results and the consequences of the Quevedo approach are not completely matched to the heat capacity results. Then, we employ a new metric for solving this problem. We show that this approach is successful and all divergencies of its Ricci scalar and phase transition points coincide. We also show that there is no phase transition for uncharged BTZ black holes.