Analytic treatment of geodesics in five-dimensional Myers-Perry space--times

TL;DR

This paper provides a complete analytical solution for geodesic equations in five-dimensional Myers-Perry space-times with equal rotation, using elliptic functions, and analyzes particle orbits.

Contribution

It introduces a comprehensive analytical approach to solving geodesic equations in higher-dimensional rotating black hole spacetimes, utilizing elliptic functions.

Findings

Analytical solutions expressed via Weierstra{ extss} elliptic functions.

Characterization of geodesic motion through polynomial zeros.

Efficient analysis of test particle orbits.

Abstract

We present the complete set of analytical solutions of the geodesic equation in the five-dimensional Myers-Perry space-time with equal rotation parameter in terms of the Weierstra{\ss}' elliptic and Weierstra{\ss}' zeta and sigma functions. We study the underlying polynomials in the polar and radial equations which depend on the parameters of the metric and conserved quantities of a test particle and characterize the motion by their zeros. We exemplify the efficiency of the analytical method on the orbits of test particles.