Capture of non-relativistic particles in eccentric orbits by a Kerr black hole

TL;DR

This paper derives approximate formulas for the critical angular momentum of non-relativistic particles in Kerr spacetime, enabling easier simulation of particle capture by black holes across various orbital inclinations.

Contribution

It provides new analytic expressions for particle capture thresholds in Kerr geometry applicable to all orbital inclinations.

Findings

Formulas are accurate over entire angular momentum range.

Applicable to arbitrary orbital inclinations.

Facilitates N-body simulations of star cluster evolution.

Abstract

We obtain approximate analytic expressions for the critical value of the total angular momentum of a non-relativistic test particle moving in the Kerr geometry, such that it will be captured by the black hole. The expressions apply to arbitrary orbital inclinations, and are accurate over the entire range of angular momentum for the Kerr black hole. The expressions can be easily implemented in N-body simulations of the evolution of star clusters around massive galactic black holes, where such captures play an important role.