Topology of black hole thermodynamics via Rényi statistics

Abstract

In this paper, we investigate the topological numbers of the four-dimensional Schwarzschild black hole, $d$-dimensional Reissner-Nordström (RN) black hole, $d$-dimensional singly rotating Kerr black hole and five-dimensional Gauss-Bonnet black hole via the Rényi statistics. We find that the topological number calculated via the Rényi statistics is different from that obtained from the Gibbs-Boltzmann (GB) statistics. However, what is interesting is that the topological classifications of different black holes are consistent in both the Rényi and GB statistics: the four-dimensional RN black hole, four-dimensional and five-dimensional singly rotating Kerr black holes, five-dimensional charged and uncharged Gauss-Bonnet black holes belong to the same kind of topological class, and the four-dimensional Schwarzschild black hole and $d(>5)$-dimensional singly rotating Kerr black holes belong to another kind of topological class. In addition, our results suggest that the topological numbers calculated via the Rényi statistics in asymptotically flat spacetime background are equal to those calculated from the standard GB statistics in asymptotically AdS spacetime background, which provides more evidence for the connection between the nonextensivity of the Rényi parameter $\lambda$ and the cosmological constant $\Lambda$.

24 pages,19 figures

References in corpus (27)

• Thermodynamics of Black Holes in Massive Gravity
• Critical phenomena and thermodynamic geometry of charged Gauss-Bonnet AdS black holes
• Black Hole Solutions as Topological Thermodynamic Defects
• Phase transition and Thermodynamical geometry of Reissner-Nordström-AdS Black Holes in Extended Phase Space
• Topological classes of thermodynamics of rotating AdS black holes
• Topology of black hole thermodynamics in Lovelock gravity
• Topological classes of rotating black holes
• Topology of critical points and Hawking-Page transition
• Zeroth Law compatibility of non-additive thermodynamics
• Consistent thermodynamics and topological classes for the four-dimensional Lorentzian charged Taub-NUT spacetimes
• Revisiting thermodynamic topologies of black holes
• Classifying topology of consistent thermodynamics of the four-dimensional neutral Lorentzian NUT-charged spacetimes
• Thermodynamic topology of 4D Dyonic AdS black holes in different ensembles
• Bardeen Black Hole Thermodynamics from Topological Perspective
• Topological interpretation for phase transitions of black holes
• Thermodynamics of Conformal Anomaly Corrected Black Holes in AdS Space
• The topological natures of the Gauss-Bonnet black hole in AdS space
• Ruppeiner thermodynamic geometry for the Schwarzschild-AdS black hole
• Topology of nonlinearly charged black hole chemistry via massive gravity
• Topological classes of black holes in de-Sitter spacetime
• Solid/Liquid Phase Transition and Heat Engine in Asymptotically Flat Schwarzschild Black Hole via the Rényi Extended Phase Space Approach
• Topological classes of higher-dimensional black holes in massive gravity
• Topology in thermodynamics of regular black strings with Kaluza-Klein reduction
• Emergent Phase, Thermodynamic Geometry and Criticality of Charged Black Holes from Rényi Statistics
• van der Waals fluid and charged AdS black hole in the Landau theory
• On Rényi universality formula of charged flat black holes from Hawking-Page phase transition
• On some phase equilibrium features of charged black holes in flat spacetime via Rényi statistics

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• Topological Insights into Black Hole Thermodynamics: Non-Extensive Entropy in CFT framework
• Black Hole Chemistry: the first 15 years
• Thermodynamic topological classes of the rotating, accelerating black holes
• Hawking-Rényi black hole thermodynamics, Kiselev solution, and cosmic censorship
• Topology of black hole thermodynamics: A brief review
• The $D$-dimensional charged AdS black holes solutions in polytropic dark energy from Barrow entropy
• Thermodynamic Topology of Black Holes within Tsallis Statistics
• Hawking-Rényi thermodynamics of rotating black holes from locally Kiselev-type behavior