Thermodynamic Topology and Phase Space Analysis of AdS Black Holes Through Non-Extensive Entropy Perspectives

TL;DR

This paper explores the thermodynamic topology of AdS black holes using non-extensive entropy frameworks, revealing how topological charges vary with different entropy parameters in bulk-boundary and restricted phase space analyses.

Contribution

It introduces a comprehensive analysis of black hole thermodynamics through various non-extensive entropy measures, highlighting topological charge transitions and classifications.

Findings

Topological charges depend on entropy parameters and vary across different entropy frameworks.

In RPS, the topological charge remains mostly positive, with some parameter-dependent variations.

Distinct entropy measures exhibit unique topological charge behaviors and transitions.

Abstract

This paper studies the thermodynamic topology through the bulk-boundary and restricted phase space (RPS) frameworks. In bulk-boundary framework, we observe two topological charges $(\omega = +1, -1)$ concerning the non-extensive Barrow parameter and with ($\delta=0$) in Bekenstein-Hawking entropy. For Renyi entropy, different topological charges are observed depending on the value of the $\lambda$ with a notable transition from three topological charges $(\omega = +1, -1, +1)$ to a single topological charge $(\omega = +1)$ as $\lambda$ increases. Also, by setting $\lambda$ to zero results in two topological charges $(\omega = +1, -1)$. Sharma-Mittal entropy exhibits three distinct ranges of topological charges influenced by the $\alpha$ and $\beta$ with different classifications viz $\beta$ exceeds $\alpha$, we will have $(\omega = +1, -1, +1)$, $\beta = \alpha$, we have $(\omega = +1, -1)$ and for $\alpha$ exceeds $\beta$ we face $(\omega = -1)$. Also, Kaniadakis entropy shows variations in topological charges viz we observe $(\omega = +1, -1)$ for any acceptable value of $K$, except when $K = 0$, where a single topological charge $(\omega = -1)$. In the case of Tsallis-Cirto entropy, for small parameter $\Delta$ values, we have $(\omega = +1)$ and when $\Delta$ increases to 0.9, we will have $(\omega = +1, -1)$. When we extend our analysis to the RPS framework, we find that the topological charge consistently remains $(\omega = +1)$ independent of the specific values of the free parameters for Renyi, Sharma-Mittal, and Tsallis-Cirto. Additionally, for Barrow entropy in RPS, the number of topological charges rises when $\delta$ increases from 0 to 0.8. Finally for Kaniadakis entropy, at small values of $K$, we observe $(\omega = +1)$. However, as the non-extensive parameter $K$ increases, we encounter different topological charges and classifications with $(\omega = +1, -1)$.