Going into a tailspin near the abyss: analytic solutions for spinning particles on near equatorial, plunging orbits in Kerr spacetime

TL;DR

This paper derives the first analytic solutions for the nearly equatorial, plunging motion of spinning particles in Kerr spacetime, including spin precession effects and corrections to the innermost bound orbit.

Contribution

It provides novel analytic solutions for spinning test particles on plunging orbits in Kerr spacetime, incorporating spin precession and a new parametrization.

Findings

Analytic solutions for nearly equatorial plunging orbits with spin.

Correction to the radius of the innermost bound circular orbit.

A Keplerian-like parametrization for generic plunging orbits.

Abstract

This work presents, the first time, analytic solutions for the nearly equatorial, plunging motion of a spinning test-particle in Kerr spacetime. The equations of motion are solved at first-order in the small-body spin for all classes of plunging orbits with energy $E < 1$. The solutions incorporate the small precession of the orbital plane caused by the precession of the particle's spin. Additionally, we present the correction to the radius of the innermost bound circular orbit in closed form, and introduce a novel, Keplerian-like parametrization for generic plunging orbits. Our solutions will be useful in the modelling of inspiral-merger-ringdown waveforms with self-force methods and black hole perturbation theory.