## Motion of particles on a \$z=2\$ Lifshitz black hole in 3+1 dimensions    [PDF]

Marco Olivares, Yerko Vásquez, J. R. Villanueva, Felipe Moncada
We study the geodesic structure of a \$z=2\$ Lifshitz black hole in 3+1 spacetime dimensions that is an exact solution to the Einstein-scalar-Maxwell theory. We investigate the motion of massless and massive particles in this background using the standard Lagrangian procedure. Analytical expressions are obtained for radial and angular motions of the test particles, where the polar trajectories are given in terms of the \$\wp\$ - Weierstrass elliptic function. It is shown that confined orbits are not allowed on this spacetime, this result agrees with the obtained recently in the literature for other Lifshitz black holes.
View original: http://arxiv.org/abs/1306.5285