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

Mohammad Ali S. Afshar; Mohammad Reza Alipour; Saeed Noori Gashti; Jafar Sadeghi

doi:10.1140/epjc/s10052-025-14173-2

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2025) 85: 457
https://doi.org/10.1140/epjc/s10052-025-14173-2

Regular Article - Theoretical Physics

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

Mohammad Ali S. Afshar¹^,2^a, Mohammad Reza Alipour¹^,3, Saeed Noori Gashti³ and Jafar Sadeghi¹^,2

¹ Department of Physics, Faculty of Basic Sciences, University of Mazandaran, P. O. Box 47416-95447, Babolsar, Iran
² Canadian Quantum Research Center, 204-3002 32 Ave, V1T 2L7, Vernon, BC, Canada
³ School of Physics, Damghan University, P. O. Box 3671641167, Damghan, Iran

^a m.a.s.afshar@gmail.com

Received: 6 January 2025
Accepted: 8 April 2025
Published online: 25 April 2025

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 $λ$ $\lambda$ (Rényi entropy) plays a crucial role in the phase behavior of black holes. Specifically, when $λ$ $\lambda$ is below the critical value (C), it has a negligible impact on the phase behavior. However, when $λ$ $\lambda$ exceeds the critical value, it significantly alters the phase transition outcomes. Determining the most physically representative values of $λ$ $\lambda$ will require experimental validation, but this parameter flexibility allows researchers to better explain black hole phase transitions under varying physical conditions. Furthermore, the parameters $α$ $\alpha$ and $β$ $\beta$ 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 $α \approx β$ $\alpha \approx \beta$ 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 $(ω = + 1, - 1)$ $(\omega = +1, -1)$ , 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.

© The Author(s) 2025

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