First laws of thermodynamics in IR Modified H\v{o}rava-Lifshitz gravity

TL;DR

This paper investigates the first law of thermodynamics in IR modified H"{o}rava-Lifshitz gravity, deriving formulas for Kehagias-Sfetsos black holes and redefining mass as a new state parameter.

Contribution

It introduces a novel approach to the first law in this gravity model by treating nd redefining mass to match ADM mass, extending thermodynamic understanding.

Findings

Derived integral and differential formulas for the first law.

Redefined mass as a new state parameter.

Confirmed consistency with ADM mass when =3/8.

Abstract

We study the first law of thermodynamics in IR modified H\v{o}rava-Lifshitz spacetime. Based on the Bekenstein-Hawking entropy, we obtain the integral formula and the differential formula of the first law of thermodynamics for the Kehagias-Sfetsos black hole by treating $\omega$ as a new state parameter and redefining a mass that is just equal to $M_{ADM}$ obtained by Myung\cite{YSM2} if we take $\alpha=3\pi/8$.