Thermodynamic Properties of Kehagias-Sfetsos Black Hole \& KS/CFT Correspondence

TL;DR

This paper investigates the thermodynamic properties of Kehagias-Sfetsos black holes in Hořava-Lifshitz gravity, revealing non-universal horizon area relations, deriving bounds, and exploring the KS/CFT correspondence.

Contribution

It provides a detailed analysis of horizon thermodynamics, bounds, and the breakdown of certain thermodynamic laws for KS black holes, and discusses the KS/CFT correspondence.

Findings

Horizon area products are not universal.

First law and Smarr relations do not hold for KS black holes.

Derived bounds on entropy and irreducible mass.

Abstract

We speculate on various thermodynamic features of the inner horizon~(${\mathcal H}^{-}$) and outer horizons~(${\mathcal H}^{+}$) of Kehagias-Sfetsos~(KS) black hole~(BH) in the background of Ho\v{r}ava Lifshitz gravity. We compute particularly the \emph{area product, area sum, area minus and area division} of the BH horizons. We find that they all are \emph{not} showing universal behavior whereas the product is a universal quantity~ [Pradhan P., \textit{Phys. Lett. B}, {\bf 747} (2015) {64}]. Based on these relations, we derive the area bound of all horizons. From the area bound we derive the entropy bound and irreducible mass bound for all the horizons~(${\mathcal H}^{\pm}$). We also observe that the \emph{First law} of BH thermodynamics and \emph {Smarr-Gibbs-Duhem } relations do not hold for this BH. The underlying reason behind this failure due to the scale invariance of the coupling constant. Moreover, we compute the \emph{Cosmic-Censorship-Inequality} for this BH which gives the lower bound for the total mass of the spacetime and it is supported by cosmic cencorship conjecture. Finally, we discuss the KS/CFT~(Conformal Field Theory) correspondence via a thermodynamic procedure.