Spacing of the entropy spectrum for KS Black hole in Horava-Lifshitz gravity

TL;DR

This paper derives the entropy spectrum for KS black holes in Hořava-Lifshitz gravity using quasi-normal modes, revealing that the mass parameter does not influence the entropy spectrum and highlighting the role of charge-like parameters.

Contribution

It introduces a method to include charge and mass explicitly in the surface gravity and QNM calculations for spherically symmetric black holes in HL gravity.

Findings

Mass parameter does not appear in the entropy spectrum.

Charge-like parameter influences surface gravity and QNM.

Method applicable to any spherically symmetric spacetime with one horizon.

Abstract

In this paper we present the spectrum of entropy/area for Kehagias-Sfetsos (KS) black hole in Ho$\check{\textbf{r}}$ava-Lifshitz (HL)gravity via quasi-normal modes (QNM) approach. We show that in the massive case the mass parameter $\mu$ disappears in the entropy spectrum and only the quasinormal modes modified by a term which is proportional to the mass square term. Our calculations show that the charge like parameter $\frac{1}{2\omega}=Q^{2}$ appears in the surface gravity and our calculations can be applied to any spherically symmetric spacetime which has only one physically acceptable horizon. Our main difference between our calculations and what was done in \cite{1} is that the portion of charge and mass is included explicitly in the surface gravity and consequently in the QNM expression. Since the imaginary part of the QNM is related to the adiabatic invariance of the system and also to the entropy, surprisingly the mass parameter do not appear in the entropy spectrum. Our conclusion supported by some acclaims about that the scalar field parameters (charges) can not change the fundamental parameters in the 4-dimensional black holes.