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

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., $\mathit{\text{Phys.}}\mathit{\text{Lett.}}\mathit{\text{B}}$, {\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.