The evolution of circular, non-equatorial orbits of Kerr black holes due to gravitational-wave emission

TL;DR

This paper studies how gravitational-wave emission causes circular, non-equatorial Kerr black hole orbits to evolve, revealing that inclination angles tend to increase and providing detailed waveform characteristics especially for rapidly spinning black holes.

Contribution

It demonstrates that the evolution of such orbits can be deduced from fluxes without local forces and compares post-Newtonian predictions with strong-field results.

Findings

Inclined orbits evolve to larger inclination angles.

Waveforms are complex, especially for rapidly spinning black holes.

Post-Newtonian estimates overpredict inclination evolution rate by up to a factor of 3.

Abstract

A major focus of much current research in gravitation theory is on understanding how radiation reaction drives the evolution of a binary system, particularly in the extreme mass ratio limit. Such research is of direct relevance to gravitational-wave sources for space-based detectors (such as LISA). We present here a study of the radiative evolution of circular (i.e., constant Boyer-Lindquist coordinate radius), non-equatorial Kerr black hole orbits. Recent theorems have shown that, at least in an adiabatic evolution, such orbits evolve from one circular configuration into another, changing only their radius and inclination angle. This constrains the system's evolution in such a way that the change in its Carter constant can be deduced from knowledge of gravitational wave fluxes propagating to infinity and down the black hole's horizon. Thus, in this particular case, a local radiation reaction force is not needed. In accordance with post-Newtonian weak-field predictions, we find that inclined orbits radiatively evolve to larger inclination angles (although the post-Newtonian prediction overestimates the rate of this evolution in the strong field by a factor $\lesssim 3$). We also find that the gravitational waveforms emitted by these orbits are rather complicated, particularly when the hole is rapidly spinning, as the radiation is influenced by many harmonics of the orbital frequencies.