Geodesic structure of Lifshitz black holes in 2+1 dimensions

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 et al. (Phys. Rev. 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 rho, sigma, and zeta functions.