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.
Categories: gr-qc hep-th