Time like geodesics in three-dimensional rotating Ho\v{r}ava AdS black hole

TL;DR

This paper investigates particle trajectories in a three-dimensional rotating Hořava AdS black hole, revealing that Lorentz violation introduces a richer geodesic structure with new orbit possibilities not present in the standard BTZ black hole.

Contribution

It provides an analytical study of geodesics in a Lorentz-violating Hořava AdS black hole, highlighting new orbital behaviors due to Lorentz symmetry breaking.

Findings

Presence of planetary and circular orbits in the Lorentz-violating black hole

Enhanced geodesic complexity compared to the standard BTZ black hole

Analytical solutions to the geodesic equations in this background

Abstract

We study the motion of particles in the background of a three-dimensional rotating Ho\v{r}ava AdS black hole that corresponds to a Lorentz-violating version of the BTZ black hole and we analyze the effect of the breaking of Lorentz invariance in such motion by solving analytically the geodesic equations. Mainly, we find that Lorentz-violating version of the BTZ black hole posses a more rich geodesic structure, where the planetary and circular orbits are allowed, which does not occurs in the BTZ background.