Thermodynamic Topology of Black Holes within Tsallis Statistics

TL;DR

This paper explores the topological thermodynamics of black holes using Tsallis non-extensive statistics, revealing how the non-extensive parameter influences stability and classifying black holes into distinct topological categories.

Contribution

It introduces a novel framework combining Tsallis statistics with topological thermodynamics to classify black hole stability and topology across different dimensions and charge states.

Findings

Black holes are classified into stable, unstable, and critical classes based on topological number W.

The non-extensive parameter delta significantly affects the thermodynamic behavior and classification.

Dimensionality does not influence the topological thermodynamics in the Tsallis framework.

Abstract

In this paper, we investigate the thermodynamic topology of black holes within the framework of Tsallis statistics. By integrating Tsallis non-extensive statistics with topological thermodynamics, we analyze the local and global stability of various black hole solutions, including Schwarzschild, Reissner-Nordstrom, and higher-dimensional black holes. The introduction of Tsallis entropy, parameterized by the non-extensive parameter delta, results in distinct thermodynamic behaviors depending on its value. Employing Duan's phi-mapping theory, we classify the thermodynamic topology of four-dimensional Schwarzschild black holes and non-charged higher-dimensional black holes into three distinct classes based on their topological number W: stable (W = +1), unstable (W = -1), and critical (W = 0). Additionally, the thermodynamic topology of Reissner-Nordstrom and charged higher-dimensional black holes is categorized into two classes, where W = +1 indicates a stable class and W = 0 represents a less stable class. Our study further demonstrates that the number of dimensions does not affect the topological thermodynamics within the context of non-extensive statistics. This approach provides novel insights into the interplay between Tsallis statistics and black hole thermodynamics, underscoring the pivotal role of topology in understanding black hole physics.