Topological insights into black hole thermodynamics: non-extensive entropy in CFT framework

Abstract

Abstract In this paper, we conducted an in-depth investigation into the thermodynamic topology of Einstein-Gauss-Bonnet black holes within the framework of Conformal Field Theory (CFT), considering the implications of non-extensive entropy formulations. Our study reveals that the parameter $$\lambda $$ λ (Rényi entropy) plays a crucial role in the phase behavior of black holes. Specifically, when $$\lambda $$ λ is below the critical value (C), it has a negligible impact on the phase behavior. However, when $$\lambda $$ λ exceeds the critical value, it significantly alters the phase transition outcomes. Determining the most physically representative values of $$\lambda $$ λ will require experimental validation, but this parameter flexibility allows researchers to better explain black hole phase transitions under varying physical conditions. Furthermore, the parameters $$\alpha $$ α and $$\beta $$ β affect the phase structure and topological charge for the Sharma–Mittal entropy. Only in the case of $$C>C_c$$ C > C c and in the condition of $$\alpha \approx \beta $$ α ≈ β will we have a first-order phase transition with topological charge + 1. Additionally, for the loop quantum gravity (LQG) non-extensive entropy as the parameter q approaches 1, the classification of topological charges changes. We observe configurations with one and three topological charges with respect to critical value C, resulting in a total topological charge $$W = +1$$ W = + 1 , and configurations with two topological charges $$(\omega = +1, -1)$$ ( ω = + 1 , - 1 ) , leading to a total topological charge $$W = 0$$ W = 0 . These findings provide new insights into the complex phase behavior and topological characteristics of black holes in the context of CFT and non-extensive entropy formulations.