A Periodic Table for Black Hole Orbits

TL;DR

This paper introduces a new classification system for black hole orbits based on a dynamical systems approach, revealing complex orbit structures and implications for gravitational wave modeling.

Contribution

It develops a novel orbit taxonomy linking periodic orbits to rational numbers, enhancing understanding of Kerr spacetime dynamics and orbit classification.

Findings

Periodic orbit taxonomy covers all orbit types.

Precessing ellipses are not present in strong-field regimes.

Zoom-whirl behavior is inevitable beyond a certain point.

Abstract

Understanding the dynamics around rotating black holes is imperative to the success of the future gravitational wave observatories. Although integrable in principle, test particle orbits in the Kerr spacetime can also be elaborate, and while they have been studied extensively, classifying their general properties has been a challenge. This is the first in a series of papers that adopts a dynamical systems approach to the study of Kerr orbits, beginning with equatorial orbits. We define a taxonomy of orbits that hinges on a correspondence between periodic orbits and rational numbers. The taxonomy defines the entire dynamics, including aperiodic motion, since every orbit is in or near the periodic set. A remarkable implication of this periodic orbit taxonomy is that the simple precessing ellipse familiar from planetary orbits is not allowed in the strong-field regime. Instead, eccentric orbits trace out precessions of multi-leaf clovers in the final stages of inspiral. Furthermore, for any black hole, there is some point in the strong-field regime past which zoom-whirl behavior becomes unavoidable. Finally, we sketch the potential application of the taxonomy to problems of astrophysical interest, in particular its utility for computationally intensive gravitational wave calculations.