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.

19 pages, 10 figures

References in corpus (15)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole
• First M87 Event Horizon Telescope Results. IV. Imaging the Central Supermassive Black Hole
• First M87 Event Horizon Telescope Results. V. Physical Origin of the Asymmetric Ring
• Joule-Thomson Expansion of Charged AdS Black Holes
• Holographic Thermodynamics Requires a Chemical Potential for Color
• Critical behaviour and microscopic structure of charged AdS black holes via an alternative phase space
• Revisiting thermodynamic topologies of black holes
• Bardeen Black Hole Thermodynamics from Topological Perspective
• Topological classification and black hole thermodynamics
• Thermodynamics of Kerr-AdS black holes in the restricted phase space
• Multi-critical Points in Black Hole Phase Transitions
• 4D-EGB Black Holes in RPS Thermodynamics
• Topology of black hole thermodynamics via Rényi statistics
• Holographic Thermodynamics of BTZ Black Holes and Tsallis Entropy

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