Thermal chaos of charged-flat black hole via R\'enyi formalism

TL;DR

This paper investigates the chaotic behavior of charged-flat black holes in Rényi extended phase space, revealing how thermal perturbations induce chaos and how black hole charge influences this transition, highlighting links to AdS black holes and nonextensive thermodynamics.

Contribution

It demonstrates the emergence of chaos in charged-flat black holes under Rényi formalism and explores the dependence on charge and perturbation parameters, connecting nonextensive statistics with black hole thermodynamics.

Findings

Chaos occurs when the parameter δ exceeds a critical value δ_c.

Larger black hole charge Q suppresses the onset of chaos.

Chaos is inevitable under space-periodic thermal perturbations regardless of amplitude.

Abstract

Charged-flat black holes in the R\'enyi extended phase space demonstrate phase structures akin to those of a van der Waals fluid in four-dimensional spacetime and mirror the behaviors of Reissner-Nordstrom-Anti-de-Sitter black holes within the standard Gibbs-Boltzmann extended phase space. This study delves into the dynamics of states initially positioned within the unstable spinodal region of the phase space associated with the charged-flat black hole when subjected to time-periodic thermal perturbations. Our analysis based on the Mel'nikov method reveals that chaos emerges when the $\delta$ parameter surpasses a critical threshold, $\delta_c$. This critical quantity is dependent on the black hole charge; notably, a larger value of $Q$ impedes the onset of chaos. Furthermore, we examine the effects of space-periodic thermal perturbations on its equilibrium state and find that chaos invariably occurs, irrespective of the perturbation amplitude. Hence, the chaotic dynamics observed in the analysis of charged-flat black holes under R\'enyi statistics exhibit resemblances to those of asymptotically AdS-charged black holes investigated via the Gibbs-Boltzmann formalism. This serves as yet another example of a potential and significant connection between the cosmological constant and the nonextensivity R\'enyi parameter.