Geodesic motion in equal angular momenta Myers-Perry-AdS spacetimes

TL;DR

This paper analyzes the geodesic motion of particles in five-dimensional equally spinning Myers-Perry-AdS black holes, revealing properties of stable orbits, ISCOs, and null orbits, with implications for black hole stability and spacetime structure.

Contribution

It provides a detailed analytical study of geodesics in five-dimensional rotating AdS black holes, including explicit solutions and stability analysis, extending understanding beyond four-dimensional cases.

Findings

ISCOs merge with the horizon at extremality

No stable null orbits outside the horizon

Stable orbits inside the horizon and around naked singularities

Abstract

We study the geodesic motion of massive and massless test particles in the background of equally spinning Myers-Perry-anti-de Sitter (AdS) black holes in five dimensions. By adopting a coordinate system that makes manifest the cohomogeneity-1 property of these spacetimes, the equations of motion simplify considerably. This allows us to easily separate the radial motion from the angular part and to obtain solutions for angular trajectories in a compact closed form. For the radial motion we focus our attention on spherical orbits. In particular, we determine the timelike innermost stable circular orbits (ISCOs) for these asymptotically AdS spacetimes, as well as the location of null circular orbits. We find that the ISCO dives below the ergosurface for black holes rotating close to extremality and merges with the event horizon exactly at extremality, in analogy with the four-dimensional Kerr case. For sufficiently massive black holes in AdS there exists a spin parameter range in which the background spacetime is stable against superradiance and the ISCO lies inside the ergoregion. Our results for massless geodesics show that there are no stable circular null orbits outside the horizon, but there exist such orbits inside the horizon, as well as around over-extremal spacetimes, i.e., naked singularities. We also discuss how these orbits deform from the static to the rotating case.