Homoclinic Orbits around Spinning Black Holes II: The Phase Space Portrait

TL;DR

This paper provides a detailed phase space analysis of homoclinic orbits around spinning black holes, including exact actions and frequencies, and introduces a reduced Hamiltonian framework for tracking orbit groups.

Contribution

It introduces a phase space portrait with exact actions and frequencies and develops a reduced Hamiltonian model for Kerr black hole orbits, enabling efficient trajectory analysis.

Findings

Exact expressions for actions and fundamental frequencies of homoclinic orbits.

A reduced Hamiltonian description for Kerr black hole motion.

Potential applications in gravitational waveform modeling.

Abstract

In paper I in this series, we found exact expressions for the equatorial homoclinic orbits: the separatrix between bound and plunging, whirling and not whirling. As a companion to that physical space study, in this paper we paint a phase space portrait of the homoclinic orbits that includes exact expressions for the actions and fundamental frequencies. Additionally, we develop a reduced Hamiltonian description of Kerr motion that allows us to track groups of trajectories with a single global clock. This facilitates a variational analysis, whose stability exponents and eigenvectors could potentially be useful for future studies of families of black hole orbits and their associated gravitational waveforms.