Thermodynamic topology of Phantom AdS black holes in massive gravity via non-extensive entropies

Abstract

In this study, we explore the topological numbers associated with Phantom AdS black holes (BHs) in massive gravity using non-extensive entropies. We analyze their characteristics using various entropy measures, including the Bekenstein–Hawking entropy, Rényi entropy, Barrows entropy, Sharma-Mittal entropy, and the logarithmic-corrected entropy. We observe that the calculated topological number ($T$) varies across different entropy measures. Nevertheless, what is particularly intriguing is the persistent coherence in the topological classification of BH, regardless of whether we consider the Rényi entropy, the logarithmic-corrected entropy or the Bekenstein–Hawking entropy.