Motion of particles on a $z=2$ Lifshitz black hole in 3+1 dimensions

Abstract

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.

11 pages, 6 figures

References in corpus (7)

• Non-relativistic holography
• Conductivity and Diffusion Constant in Lifshitz Backgrounds
• On the thermodynamics of Lifshitz black holes
• On the Null Trajectories in Conformal Weyl Gravity
• Geodesic Structure of Lifshitz Black Holes in 2+1 Dimensions
• Massive neutral particles on heterotic string theory
• About the coordinate time for photons in Lifshitz Space-times

Cited by in corpus (5)

• Formation of Molecular Clouds and Global Conditions for Star Formation
• Scalar field perturbations of a Lifshitz black hole in conformal gravity in three dimensions
• Gravitational Rutherford scattering and Keplerian orbits for electrically charged bodies in heterotic string theory
• Periapsis shift and deflection of light by hairy black holes
• Generalized Thermodynamic Properties of Lifshitz black holes