Geodesic equations for particles and light in the black spindle spacetime

Abstract

In this paper, we derive the geodesic equation for massive particles and light for the black spindle spacetime. The solution for light can be formulated in terms of the Weierstraß ℘-, σ-, and ζ-function, whereas a part of the solutions for massive particles is given in terms of derivatives of the Kleinian σ-function. We analyze the possible orbit types using parametric diagrams and effective potentials. Furthermore, we visualize the orbits in a coordinate system, where the spindle-like topology of the horizon is visible.