https://doi.org/10.1140/epjc/s10052-024-13511-0
Regular Article - Theoretical Physics
Riemann surfaces and winding numbers of Rényi phase structure of charged-flat black holes
1
LPTHE, Physics Department, Faculty of Sciences, Ibnou Zohr University, Agadir, Morocco
2
Faculty of Sciences Ain Chock, Laboratory of High Energy Physics and Condensed Matter HASSAN II University, Casablanca, Morocco
3
CRMEF, Regional Center for Education and Training Professions, Marrakesh, Morocco
Received:
13
August
2024
Accepted:
14
October
2024
Published online:
4
November
2024
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 nonextensive 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.
© The Author(s) 2024
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