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arXiv · 2508.07357

On Rényi Microstructural Aspects of Asymptotically Flat Charged Black Holes: A Novel Duality

F. Barzi·H. El Moumni·K. Masmar
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Abstract

We explore the microstructure of asymptotically flat charged black holes through the lens of nonextensive Rényi statistics. A modified form of the Rényi entropy is proposed to incorporate compressibility effects, and geometrothermodynamics is applied within such a framework. Besides, by quantizing the black hole horizon area, we derive a microscopic description in terms of discrete degrees of freedom, with Rényi entropy providing a nonextensive generalization of the Bekenstein-Hawking entropy. We compute the Rényi partition function and probability distribution in the canonical ensemble, highlighting significant deviations from Boltzmann-Gibbs behavior at finite temperature due to nonextensive effects. The black hole undergoes a first-order Van der Waals-like phase transition between small and large configurations, characterized by discontinuities in entropy and latent heat, both of which are shown to depend on the number of area quanta. A critical threshold emerges beyond which the transition becomes athermal. Additionally, we establish a thermodynamic duality between charged-AdS black holes in Boltzmann-Gibbs statistics and charged-flat Rényi black holes, expressed via a conformal transformation of state variables. This duality extends naturally to higher dimensions. Our results provide new insights into the microstructure of black holes.

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F. Barzi, H. El Moumni, K. Masmar. 2025-08-10. On Rényi Microstructural Aspects of Asymptotically Flat Charged Black Holes: A Novel Duality. https://arxiv.org/abs/2508.07357

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