Comparing effective-one-body and Mathisson-Papapetrou-Dixon results for a spinning test particle on circular equatorial orbits around a Kerr black hole

TL;DR

This paper compares two theoretical models for a spinning test particle orbiting a Kerr black hole, analyzing their predictions for orbital constants and gravitational-wave fluxes, with implications for improving gravitational wave modeling.

Contribution

It provides a detailed comparison between the MPD formalism and the EOB Hamiltonian for spinning particles in Kerr spacetime, highlighting differences in flux predictions.

Findings

No flux difference in Schwarzschild background

Maximum flux difference occurs for large positive spins in Kerr

Results inform future EOB model improvements for GW detection

Abstract

We consider a spinning test particle around a rotating black hole and compare the Mathisson-Papapetrou-Dixon (MPD) formalism under the Tulczyjew-Dixon spin supplementary condition to the test-mass limit of the effective-one-body (EOB) Hamiltonian of [Phys. Rev. D.90, 044018(2014)], with enhanced spin-orbit sector. We focus on circular equatorial orbits: we first compare the constants of motion at their linear in secondary spin approximation and then we compute the gravitational-wave (GW) fluxes using a frequency domain Teukolsky equation solver. We find no difference between the EOB and MPD fluxes when the background spacetime is Schwarzschild, while the difference for a Kerr background is maximum for large, positive spins. Our work could be considered as a first step to improve the radiation reaction of the EOB model, in view of the needs of the next-generation of GW detectors.