On R\'enyi Microstructural Aspects of Asymptotically Flat Charged Black Holes: A Novel Duality

TL;DR

This paper investigates the microstructure of asymptotically flat charged black holes using nonextensive Rényi statistics, revealing phase transitions, a thermodynamic duality, and the impact of nonextensivity on black hole thermodynamics.

Contribution

It introduces a modified Rényi entropy framework for black holes, establishes a duality with AdS black holes, and analyzes phase transitions considering nonextensive effects.

Findings

Black holes exhibit Van der Waals-like phase transitions.

A thermodynamic duality between Rènyi and Boltzmann-Gibbs black holes is established.

Nonextensive effects significantly alter black hole thermodynamic behavior.

Abstract

We explore the microstructure of asymptotically flat charged black holes through the lens of nonextensive R\'enyi statistics. A modified form of the R\'enyi 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 R\'enyi entropy providing a nonextensive generalization of the Bekenstein-Hawking entropy. We compute the R\'enyi 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 R\'enyi 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.