Thermodynamics and phase transition structure of charged black holes in f(R) gravity background from Rényi statistics perception

Abstract

In the current study, we investigate the Rényi statistics as an extension of the Boltzmann-Gibbs theory, in order to characterize the non-Boltzmannian phase structure of charged black holes in the f(R) gravity. Through this research, we discover that a Hawking-Page phase transition and a Van-der-Waals phase portrait, which are missing from the standard Boltzmann-Gibbs' description, emerge respectively within the grand canonical ensemble and canonical ensemble via the Rényi formalism.The thermodynamics associated with charged black holes without cosmological constant black holes using Rényi statistics processes the same properties as those of asymptotically AdS charged black holes via Gibbs-Boltzmann formalism, as further evidenced by such phase structures found here. This is another example of a potential and substantial relationship between the cosmological constant and the nonextensive Rényi parameter.