Particles motion on topological Lifshitz black holes in 3+1 dimensions

TL;DR

This paper analyzes the motion of particles around topological Lifshitz black holes in 3+1 dimensions, revealing that confined orbits are forbidden and radial photons can escape to infinity in finite coordinate time.

Contribution

It provides an analytical study of geodesic motion in Lifshitz black hole spacetimes, highlighting novel escape behaviors of photons and the absence of confined orbits.

Findings

Confined orbits are forbidden in this spacetime.

Radial photons can escape to infinity in finite coordinate time.

Analytical geodesic solutions for massive and massless particles.

Abstract

In the present paper we study the causal structure of a topological black hole presented by Mann R. B. JHEP 06, 075 (2009) by mean the standard Lagrangian procedure, which allow us analyze qualitatively the behavior of test particles using the effective potential. Then, the geodesic motion of massive and massless particles is obtained analytically. We find that confined orbits are forbidden on this spacetime, however radial photons can escape to infinity in an infinite proper time but in a finite coordinate time, this correspond to an interesting and novel result.