Five-Dimensional Black Hole Capture Cross-Sections

TL;DR

This paper analyzes how particles are scattered and captured by five-dimensional rotating black holes, deriving conditions for capture and visualizing the capture surface as black hole rotation varies.

Contribution

It provides the first detailed analysis of particle capture cross-sections in five-dimensional Myers-Perry black holes, including impact parameter impact and deformation due to rotation.

Findings

Capture surface is a sphere for non-rotating black holes.

Rotation deforms the capture surface, especially at high rotation.

Asymptotic expressions describe small rotational deformations.

Abstract

We study scattering and capture of particles by a rotating black hole in the five-dimensional spacetime described by the Myers-Perry metric. The equations of geodesic motion are integrable, and allow us to calculate capture conditions for a free particle sent towards a black hole from infinity. We introduce a three-dimensional impact parameter describing asymptotic initial conditions in the scattering problem for a given initial velocity. The capture surface in impact parameter space is a sphere for a non-rotating black hole, and is deformed for a rotating black hole. We obtain asymptotic expressions that describe such deformations for small rotational parameters, and use numerical calculations to investigate the arbitrary rotation case, which allows us to visualize the capture surface as extremal rotation is approached.