Spinning particles near Kerr black holes: Orbits and gravitational-wave fluxes through the Hamilton-Jacobi formalism

TL;DR

This paper develops a new semi-analytical method using the Hamilton-Jacobi formalism to model spinning particles in Kerr spacetime, improving accuracy and speed in gravitational-wave flux calculations for extreme mass-ratio inspirals.

Contribution

It introduces a novel solver for the Mathisson-Papapetrou-Dixon equations and provides the first analytic expressions for spin corrections and waveform effects including precession.

Findings

New semi-analytical expressions for spin corrections to orbits.

Enhanced speed and accuracy over previous models.

First inclusion of full precessing secondary spin effects in waveforms.

Abstract

Extreme mass-ratio inspirals are among the key sources of gravitational waves for the Laser Interferometer Space Antenna space-based gravitational-wave detector. Achieving sufficient accuracy in the gravitational-wave template for these binaries requires modeling the effects of the spin of the comparably light secondary compact object. In this work, we employ the solution of the Hamilton-Jacobi equations for the motion of spinning bodies in Kerr space-time for the first time to obtain general bound orbits. Specifically, we implement a new solver for the Mathisson-Papapetrou-Dixon equations of motion reduced to first-order form. Our approach provide novel semianalytical expressions for the spin corrections to the orbital motion and frequencies, valid for any choice of referential geodesics, and new analytic expressions for the constants of motion shifts. Then, using the Teukolsky formalism, we compute gravitational-wave energy and angular-momentum fluxes sourced by these orbits valid to linear order in secondary spin and provide waveform snapshots corresponding to the motion. The solver and the novel method we have developed substantially improve on previous studies in terms of speed and accuracy. Additionally, we include the full effect of a general precessing secondary spin in the waveform for the first time. As such, it provides a breakthrough building block for the modeling of waveforms of precessing compact binaries at large mass ratios.