Analytic solutions of the geodesic equation for U(1)^2 dyonic rotating black holes

TL;DR

This paper derives and solves the geodesic equations for U(1)^2 dyonic rotating black holes, providing explicit solutions and analyzing possible particle and light orbits.

Contribution

It presents exact analytical solutions to the geodesic equations in this complex black hole spacetime using advanced mathematical functions.

Findings

Explicit solutions in terms of Kleinian sigma-function

Classification of possible orbits using parametric diagrams

Analysis of test particle and light trajectories

Abstract

In this article we derive the geodesic equations in the $\text{U(1)}^2$ dyonic rotating black hole spacetime. We present their solutions in terms of the Kleinian $\sigma$-function and in special cases in terms of the Weierstra{\ss} $\wp$-, $\sigma$- and $\zeta$-functions. To give a list of all possible orbits, we analyse the geodesic motion of test particles and light using parametric diagrams and effective potentials.