Motion and trajectories of photons in a three-dimensional rotating Hořava AdS black hole

Abstract

We study the motion of photons in the background of a three-dimensional rotating Hořava 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.

16 pages, 12 figures, references added, minor changes, accepted for publication in PRD

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• Null geodesics in five-dimensional Reissner-Nordström anti-de Sitter black hole
• Time like geodesics in three-dimensional rotating Hořava AdS black hole
• Self-interacting scalar field in (2+1) dimensions Einstein gravity with torsion