Geodesic Motion in the (Charged) Doubly Spinning Black Ring Spacetime

TL;DR

This paper investigates the paths of particles and light around five-dimensional charged doubly spinning black rings, providing analytical solutions for special geodesic cases and analyzing their orbital behaviors.

Contribution

It offers the first analytical solutions for specific geodesics in charged doubly spinning black ring spacetimes, focusing on special cases where the Hamilton-Jacobi equation is separable.

Findings

Analytical solutions for null geodesics in the ergosphere.

Effective potential analysis of particle and light orbits.

Insights into orbital structures around charged doubly spinning black rings.

Abstract

In this article we analyze the geodesics of test particles and light in the five dimensional (charged) doubly spinning black ring spacetime. Apparently it is not possible to separate the Hamilton-Jacobi-equation for (charged) doubly spinning black rings in general, so we concentrate on special cases: null geodesics in the ergosphere and geodesics on the two rotational axes of the (charged) doubly spinning black ring. We present analytical solutions to the geodesic equations for these special cases. Using effective potential techniques we study the motion of test particles and light and discuss the corresponding orbits.