Thermodynamic topology of black holes within Tsallis statistics

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–Nordström, and higher-dimensional black holes. The introduction of Tsallis entropy, parameterized by the non-extensive parameter, δ , results in distinct thermodynamic behaviors depending on its value. Employing Duan's ϕ -mapping theory, we classify the thermodynamic topology of four-dimensional Schwarzschild black holes and non-charged higher-dimensional uncharged 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–Nordström and charged higher-dimensional charged 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.