Thermodynamic topology of black holes within Tsallis statistics

Résumé fourni par la source

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.

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