Geodesic motion in the five-dimensional Myers-Perry-AdS spacetime

TL;DR

This paper analyzes the paths of particles and light in a five-dimensional rotating anti-de Sitter black hole spacetime, deriving solutions and classifying possible orbits, with implications for the AdS/CFT correspondence.

Contribution

It provides explicit solutions for geodesic equations in five-dimensional Myers-Perry-AdS spacetime and classifies all orbit types using parametric diagrams and effective potentials.

Findings

Derived geodesic equations in closed form using Weierstraß functions

Classified all possible orbit types for different geodesic classes

Explored the photon region and spacelike geodesics in relation to AdS/CFT

Abstract

In this article we study the geodesic motion of test particles and light in the five-dimensional Myers-Perry-anti de Sitter spacetime. We derive the equations of motion and present their solutions in terms of the Weierstra{\ss} $\wp$-, $\sigma$- and $\zeta$-functions. With the help of parametric diagrams and effective potentials we analyze the geodesic motion and give a list of all possible orbit types for timelike, null and spacelike geodesics. We plot examples of the orbits and take a look at the photon region in five dimensions. Furthermore we study spacelike geodesics and their relation to the AdS/CFT correspondence.