Resonant islands of effective-one-body dynamics

Che-Yu Chen, Feng-Li Lin, Avani Patel 2022 Physical Review D 106, 084064 (2022)  

We study the chaotic signatures of the geodesic dynamics of a nonspinning test particle in the effective-one-body (EOB) formalism for the inspiral process of spinning binary black holes. We first show that the second-order post-Newtonian (2PN) EOB dynamics is nonintegrable by demonstrating that the EOB metric does not satisfy the criterion for the existence of the Carter constant. We then employ the numerical study to find the plateaus of the rotation curve, which are associated with the existence of Birkhoff islands in the Poincaré surface of section, signifying the chaotic dynamics in the system. Our results show the signatures of chaos for the EOB dynamics, especially in the regime of interest for which the Kerr bounds of the component black holes hold. We also find that chaotic behavior is more obvious as the spin parameter $a$ of the deformed EOB background metric increases. Our results can help to uncover the implications of dynamical chaos in gravitational wave astronomy. Finally, we also present some preliminary results due to corrections at 3PN order.