The Interconnection of Cosmological Constant and R\'enyi Entropy in Kalb-Ramond Black Holes: Insights from Thermodynamic Topology

Abstract

This paper seeks to establish a connection between the cosmological constant and R\'enyi entropy within the framework of Kalb-Ramond (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 R\'enyi 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 R\'enyi 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 R\'enyi parameter. We derive an approximate relationship between the R\'enyi parameter and the cosmological constant, which is consistent with similar findings in the literature from a cosmological perspective.