Riemann Surfaces and Winding Numbers of Rényi Phase Structure of Charged-Flat Black Holes
arXiv:2408.05870 · doi:10.1140/epjc/s10052-024-13511-0
Abstract
It's widely recognized that the free energy landscape captures the essentials of thermodynamic phase transitions. In this work, we extend the findings of [1] by incorporating the nonextensive nature of black hole entropy. Specifically, the connection between black hole phase transitions and the winding number of Riemann surfaces derived through complex analysis is extended to the Rényi entropy framework. This new geometrical and non-extensive formalism is employed to predict the phase portraits of charged-flat black holes within both the canonical and grand canonical ensembles. Furthermore, we elucidate novel relations between the number of sheets comprising the Riemann surface of the Hawking-Page and Van der Waals transitions and the dimensionality of black hole spacetimes. Notably, these new numbers are consistent with those found for charged-AdS black holes in Gibbs-Boltzmann statistics, providing another significant example of the potential connection between the cosmological constant and the nonextensive Rényi parameter.
19 figures, 39 pages
References in corpus (27)
- Black Hole Solutions as Topological Thermodynamic Defects
- Topology of black hole thermodynamics
- Topological classes of thermodynamics of rotating AdS black holes
- Topology of black hole thermodynamics in Lovelock gravity
- Topological classes of rotating black holes
- Zeroth Law compatibility of non-additive thermodynamics
- Topology of critical points and Hawking-Page transition
- Consistent thermodynamics and topological classes for the four-dimensional Lorentzian charged Taub-NUT spacetimes
- Classifying topology of consistent thermodynamics of the four-dimensional neutral Lorentzian NUT-charged spacetimes
- Area-law versus Rényi and Tsallis black hole entropies
- Topological classes of thermodynamics of the four-dimensional static accelerating black holes
- Thermodynamics and Van der Waals Phase Transition of Charged Black Holes in Flat Space via Rényi Statistics
- 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
- Effective thermodynamical system of Schwarzschild-de Sitter black holes from Rényi statistics
- Generalized Uncertainty Principle Impact on Nonextensive Black Hole Thermodynamics
- Continuous phase transition and microstructure of charged AdS black hole with quintessence
- Equilibrium Temperature for Black Holes with Nonextensive Entropy
- Emergent Phase, Thermodynamic Geometry and Criticality of Charged Black Holes from Rényi Statistics
- On Rényi universality formula of charged flat black holes from Hawking-Page phase transition
- Topology of Born-Infeld-AdS Black Hole Phase Transitions: Bulk and CFT Sides
- Thermodynamics of Asymptotically de-Sitter Black Hole in dRGT Massive Gravity from Rényi entropy
- Generalized Maxwell equal area law and black holes in complex free energy
- On some phase equilibrium features of charged black holes in flat spacetime via Rényi statistics
- Thermodynamic phase transition and winding number for the third-order Lovelock black hole
- AdS to dS phase transition mediated by thermalon in Einstein-Gauss-Bonnet gravity from Renyi statistics
- Thermodynamics of Black String from Rényi entropy in de Rham-Gabadadze-Tolley Massive Gravity Theory