On some phase equilibrium features of charged black holes in flat spacetime via R\'enyi statistics

TL;DR

This paper investigates the phase structure and critical phenomena of charged black holes in flat spacetime using Rényi statistics, revealing phase transition characteristics and potential links between nonextensivity and cosmology.

Contribution

It introduces a Rényi statistics framework to analyze black hole thermodynamics, extending phase space and uncovering critical behavior and a novel connection to the cosmological constant.

Findings

Critical exponent near the phase transition is 1/2.

Phase diagrams and coexistence curves are determined.

A potential link between Rényi parameter and cosmological constant is proposed.

Abstract

Motivated by the nonextensive nature of entropy in gravitational context and the Gauge/Gravity duality, black hole thermodynamics has been attracting intense emphasis in the literature. Along the present work, we investigate some features of the phase structure and critical phenomena of the 4-dimensional charged black holes in asymptotically flat spacetime within the formalism of R\'enyi statistics. First, we explore the extended phase space via the R\'enyi statistics approach. Concretely, based on the modified version of the Smarr formula, we recall the equal-area law to remove the oscillatory non-physical region in the $P_R-V$ and $T_R-S_R$ planes. Then, the coexistence curves are determined, as well as the latent heat of phase change. Moreover, we prove that the critical exponent describing the behavior of the order parameter near the critical point is $\frac{1}{2}$, which is consistent with Landau's theory of continuous phase transition. Lastly, we apply the Hamiltonian approach to R\'enyi thermodynamics which provides a new and solid mathematical basis for the extension of phase space and puts more insight into an expected and profound possible connection between the nonextensivity R\'enyi parameter $\lambda$ and the cosmological constant $ \Lambda$.