Resonant Islands of Effective-One-Body Dynamics

TL;DR

This paper investigates chaotic behavior in the effective-one-body (EOB) model of binary black hole inspirals, demonstrating non-integrability and chaos signatures, especially with increasing spin, which impacts gravitational wave analysis.

Contribution

It shows that 2PN EOB dynamics is non-integrable and identifies chaos signatures, advancing understanding of dynamical complexity in gravitational wave sources.

Findings

EOB metric does not satisfy Carter constant criterion.

Chaotic signatures are evident in the Poincaré sections.

Chaos increases with higher spin parameter a.

Abstract

We study the chaotic signatures of the geodesic dynamics of a non-spinning 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 non-integrable by demonstrating that the EOB metric does not satisfy the criterion for the existence of 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 Poincar\'e 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.