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-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.