# Geodesics and periodic orbits in Kehagias-Sfetsos black holes in deformed Ho\u{r}ava-Lifshitz gravity

## TL;DR

This paper investigates the motion of particles around Kehagias-Sfetsos black holes in deformed Hořava-Lifshitz gravity, analyzing stable orbits and periodic trajectories to distinguish these black holes from Schwarzschild ones.

## Contribution

It provides a detailed analysis of particle orbits in Kehagias-Sfetsos black holes, highlighting how orbit parameters vary with the gravity parameter and comparing with Schwarzschild black holes.

## Key findings

- Marginally bound orbits' radius and angular momentum decrease with parameter ω.
- Innermost stable circular orbits' energy and angular momentum decrease with ω.
- Periodic orbits have lower energy compared to Schwarzschild black holes.

## Abstract

The motion of a massive test particle around a Kehagias-Sfetsos black hole in deformed Ho\u{r}ava-Lifshitz gravity is studied. Employing the effective potential, the marginally bound orbits and the innermost stable circular orbits are analyzed. For the marginally bound orbits, their radius and angular momentum decrease with the parameter $\omega$ of the gravity. For the innermost stable circular orbits, the energy and angular momentum also decrease with $\omega$. Based on these results, we investigate the periodic orbits in the Kehagias-Sfetsos black holes. It is found that the apsidal angle parameter increases with the particle energy, while decreases with the angular momentum. Moreover, compared to the Schwarzschild black hole, the periodic orbits in Kehagias-Sfetsos black holes always have lower energy. These results provide us a possible way to distinguish the Kehagias-Sfetsos black hole in deformed Ho\u{r}ava-Lifshitz gravity from the Schwarzschild black hole.