Dynamics of Black Hole Pairs II: Spherical Orbits and the Homoclinic Limit of Zoom-Whirliness

TL;DR

This paper investigates the properties of spherical and homoclinic orbits in spinning black hole pairs, highlighting their significance for understanding dynamical behaviors, testing approximations, and providing initial data for simulations.

Contribution

It introduces the concept of spherical orbits in misaligned spins, analyzes the homoclinic limit as a boundary between inspiral and plunge, and discusses implications for chaos with spin-spin coupling.

Findings

Spherical orbits form a key energetic framework for black hole dynamics.

Homoclinic orbits represent the infinite whirl limit and separatrix for inspiral and plunge.

Potential for chaos arises when spin-spin interactions are included.

Abstract

Spinning black hole pairs exhibit a range of complicated dynamical behaviors. An interest in eccentric and zoom-whirl orbits has ironically inspired the focus of this paper: the constant radius orbits. When black hole spins are misaligned, the constant radius orbits are not circles but rather lie on the surface of a sphere and have acquired the name "spherical orbits". The spherical orbits are significant as they energetically frame the distribution of all orbits. In addition, each unstable spherical orbit is asymptotically approached by an orbit that whirls an infinite number of times, known as a homoclinic orbit. A homoclinic trajectory is an infinite whirl limit of the zoom-whirl spectrum and has a further significance as the separatrix between inspiral and plunge for eccentric orbits. We work in the context of two spinning black holes of comparable mass as described in the 3PN Hamiltonian with spin-orbit coupling included. As such, the results could provide a testing ground of the accuracy of the PN expansion. Further, the spherical orbits could provide useful initial data for numerical relativity. Finally, we comment that the spinning black hole pairs should give way to chaos around the homoclinic orbit when spin-spin coupling is incorporated.