Geodesic structure of Lifshitz black holes in 2+1 dimensions

Norman Cruz; Marco Olivares; J. R. Villanueva

doi:10.1140/epjc/s10052-013-2485-8

EPJ

Geodesic structure of Lifshitz black holes in 2+1 dimensions

Norman Cruz¹, Marco Olivares² and J. R. Villanueva³^,4^*

¹ Departamento de Física, Facultad de Ciencia, Universidad de Santiago de Chile, Casilla 307, Santiago, Chile
² Instituto de Física, Pontificia Universidad de Católica de Valparaíso, Av. Universidad 330, Curauma, Valparaíso, Chile
³ Departamento de Física y Astronomía, Facultad de Ciencias, Universidad de Valparaíso, Gran Bretaña 1111, Valparaíso, Chile
⁴ Centro de Astrofísica de Valparaíso, Gran Bretaña 1111, Playa Ancha, Valparaíso, Chile

Received: 8 May 2013
Published online: 4 July 2013

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 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 ℘, σ, and ζ functions.