Motion and trajectories of photons in a three-dimensional rotating Ho\v{r}ava AdS black hole

TL;DR

This paper investigates photon trajectories in a three-dimensional rotating Hořava AdS black hole, revealing how Lorentz violation influences null geodesics and allows new orbit types, with photons reaching infinity in finite coordinate time.

Contribution

It provides an analytical study of photon motion in a Lorentz-violating black hole background, highlighting new orbit possibilities due to parameter tuning.

Findings

Existence of unstable circular orbits under certain parameters

Photons reach spatial infinity in finite coordinate time

Lorentz violation alters null geodesic structure

Abstract

We study the motion of photons 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 on the null geodesics structure, by solving analytically the equations of motion. Mainly we find that, through a fine tuning of the parameters of the theory, new kinds of orbits are allowed, such as unstable circular orbits and trajectories of first kind. Also, we show that an external observer will see that photons arrive at spatial infinity in a finite coordinate time.