Holographic Thermodynamics of BTZ Black Holes and Tsallis Entropy

TL;DR

This paper explores the thermodynamics of charged BTZ black holes using holographic extended thermodynamics and Tsallis statistics, revealing stability conditions, phase behavior, and the influence of the central charge and Tsallis parameter.

Contribution

It introduces a novel thermodynamic framework incorporating conformal factors and Tsallis statistics to analyze lower-dimensional black holes, highlighting new stability and phase transition insights.

Findings

Black holes are stable for Tsallis parameter < 2.

No phase transitions occur in the classical BTZ black hole thermodynamics.

The central charge affects the thermal evolution and stability of black holes.

Abstract

This paper presents a detailed study of the thermodynamics of charged BTZ black holes using the conformal holographic extended thermodynamics formalism and Tsallis statistics. The cornerstone of our thermodynamic framework is the re-scaling of CFT by the conformal factor, which is considered a thermodynamic parameter. Here, the AdS radius is distinct from the CFT radius, allowing for independent variations of the central charge and volume. Our analysis revealed that the thermodynamic behavior of charged BTZ black holes in three dimensions is characterized by the stability and absence of phase transitions, contrasting with the behavior of four-dimensional black holes. The central charge of CFT notably influences the thermal evolution of these black holes, with a smaller central charge leading to faster thermal processes. Additionally, the temperature of large black holes is proportional to their entropy. By incorporating Tsallis statistics into our study, we found that the stability of black holes depends on the Tsallis parameter. Black holes are always stable when the Tsallis parameter is less than 2. However, if this parameter is greater than 2, a first-order phase transition occurs between small stable and large unstable. Overall, our findings contribute to a deeper understanding of the holographic thermodynamics of lower-dimensional black holes and the impact of non-extensive statistics on their physical properties.