Geodesic equations for particles and light in the black spindle spacetime

Understand

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 Weierstra{\ss} {\wp}-, {\sigma}- and {\zeta}-function, whereas a part of the solutions for massive particles is given in terms of derivatives of the Kleinian {\sigma}-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.