Geodesic Structure of Lifshitz Black Holes in 2+1 Dimensions

Abstract

We present a study of the geodesic equations of a black hole space-time which is a solution of the three-dimensional NMG theory and is asymptotically Lifshitz with $z=3$ and $d=1$ as found in [Ayon-Beato E., Garbarz A., Giribet G. and Hassaine M., Phys. Rev. {\bf D} 80, 104029 (2009)]. By means of the corresponding effective potentials for massive particles and photons we find the allowed motions by the energy levels. Exact solutions for radial and non-radial geodesics are given in terms of the Weierstrass elliptic $\wp$, $\sigma$, and $\zeta$ functions.

10 pages, 6 figures, accepted for publication in Eur. Phys. J. C

References in corpus (3)

• Massive Gravity in Three Dimensions
• Black holes in asymptotically Lifshitz spacetime
• Ghost-free, finite, fourth order D=3 (alas) gravity

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