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We study the motion of photons in the background of a three-dimensionalrotating Ho\v{r}ava AdS black hole that corresponds to a Lorentz-violatingversion of the BTZ black hole and we analyze the effect of the breaking ofLorentz invariance on the null geodesics structure, by solving analytically theequations of motion. Mainly we find that, through a fine tuning of theparameters of the theory, new kinds of orbits are allowed, such as unstablecircular orbits and trajectories of first kind. Also, we show that an externalobserver will see that photons arrive at spatial infinity in a finitecoordinate time.

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