Geodesic equations for particles and light in the black spindle spacetime

TL;DR

This paper derives geodesic equations for particles and light in the black spindle spacetime, providing solutions using special functions, analyzing orbit types, and visualizing the orbits to understand the spacetime's topology.

Contribution

It introduces explicit solutions for geodesics in black spindle spacetime using advanced mathematical functions and analyzes orbit structures and topology.

Findings

Solutions for light involve Weierstraß functions

Massive particle solutions involve Kleinian σ-functions

Orbit types are classified using parametric diagrams and potentials

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 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.