Topological Insights into Black Hole Thermodynamics: Non-Extensive Entropy in CFT framework

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 $\lambda$ (Rényi entropy) plays a crucial role in the phase behavior of black holes. Specifically, when $\lambda$ is below the critical value (C), it has a negligible impact on the phase behavior. However, when $\lambda$ exceeds the critical value, it significantly alters the phase transition outcomes. Determining the most physically representative values of $\lambda$ will require experimental validation, but this parameter flexibility allows researchers to better explain black hole phase transitions under varying physical conditions. Furthermore, the parameters $\alpha$ and $\beta$ affect the phase structure and topological charge for the Sharma-Mittal entropy. Only in the case of $C>C_c$ and in the condition of $\alpha \approx \beta$ will we have a first-order phase transition with topological charge + 1. Additionally, for the loop quantum gravity 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 $W=+1$, and configurations with two topological charges $(\omega =+1,-1)$, leading to a total topological charge $W=0$. 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.

arXiv comment17 pages, 12 figures

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• Kramer's Escape Rate and Phase Transition Dynamics in AdS Black Holes
• Assessing WGC Compatibility in ModMax Black Holes via Photon Spheres Analysis and WCCC Validation
• Thermodynamic Topological Classes of Family of Black Holes with NUT-Charge
• Infrared Extended Uncertainty Principle Corrections and Quintessence-Induced Topology of Reissner-Nordström AdS Black Holes
• Topology of black hole thermodynamics: A brief review
• A Deep Dive into classical and Topological CFT Thermodynamics in Lifshitz and Hyperscaling Violating Black Holes
• Overcoming Barriers: Kramers' Escape Rate Analysis of Metastable Dynamics in First-Order Multi-Phase Transitions
• Schwarzschild-AdS Black Holes with Cloud of Strings and Quintessence: Geodesics, Thermodynamic Topology, and Quasinormal Modes
• Topological perspective on bulk boundary thermodynamic equivalence