The Interconnection of Cosmological Constant and Renyi Entropy in Kalb-Ramond Black Holes : Insights from Thermodynamic Topology

TL;DR

This study explores the relationship between the cosmological constant and Renyi entropy in Kalb-Ramond black holes, revealing topological equivalences and deriving a connection between the Renyi parameter and the cosmological constant.

Contribution

It establishes a novel link between the cosmological constant and Renyi entropy through thermodynamic topology in Kalb-Ramond black holes, unifying different statistical frameworks.

Findings

Topological equivalence of K-R black holes in different frameworks

Derived relationship between Renyi parameter and cosmological constant

Evidence supporting the connection from thermodynamic topology

Abstract

This paper seeks to establish a connection between the cosmological constant and Renyi entropy within the framework of Kalb-Raymond(K-R) gravity. Our analysis is supported by evidence showing the equivalence of the thermodynamic topology of K-R AdS black holes in the Gibbs-Boltzmann (GB) statistical framework and K-R flat black holes in the Renyi statistical framework. We begin by exploring the thermodynamic topology of K-R black holes in flat spacetimes, focusing on the topological characteristics and phase transition behavior in both statistical frameworks. We find that K-R flat black holes in Renyi statistics exhibit equivalent global and local topological properties to K-R AdS black holes in GB statistics. This equivalence points to a potential connection between the cosmological constant and the Renyi parameter. We derive an approximate relationship between the Renyi parameter and the cosmological constant, which is consistent with similar findings in the literature from a cosmological perspective.