Spinning test body orbiting around a Kerr black hole: Eccentric equatorial orbits and their asymptotic gravitational-wave fluxes

TL;DR

This paper develops a method to compute gravitational-wave fluxes from a spinning body in eccentric equatorial orbit around a Kerr black hole, using frequency and time domain Teukolsky formalisms, and validates the results with numerical simulations.

Contribution

It introduces a new approach to calculate orbital trajectories and gravitational-wave fluxes for spinning bodies in Kerr spacetime, combining frequency and time domain techniques.

Findings

Validated flux calculations with Teukode simulations.

Derived orbital frequencies for spinning particles in Kerr.

Provided a comprehensive framework for gravitational-wave flux estimation.

Abstract

We use the frequency and time domain Teukolsky formalism to calculate gravitational-wave fluxes from a spinning body on a bound eccentric equatorial orbit around a Kerr black hole. The spinning body is represented as a point particle following the pole-dipole approximation of the Mathisson-Papapetrou-Dixon equations. Reformulating these equations we are not only able to find the trajectory of a spinning particle in terms of its constants of motion, but also to provide a method to calculate the azimuthal and the radial frequency of this trajectory. Using these orbital quantities, we introduce the machinery to calculate through the frequency domain Teukolsky formalism the energy and the angular momentum fluxes at infinity, and at the horizon, along with the gravitational strain at infinity. We crosscheck the results obtained from the frequency domain approach with the results obtained from a time domain Teukolsky equation solver called Teukode.