The deterministic nature of conservative post-Newtonian accurate dynamics of compact binaries with leading order spin-orbit interaction

TL;DR

This paper proves that conservative second post-Newtonian dynamics of spinning compact binaries with leading order spin-orbit effects are non-chaotic and integrable in specific cases, contrasting with some numerical chaos observations.

Contribution

It demonstrates the integrability of PN accurate binary dynamics with leading order spin-orbit effects in two key scenarios, clarifying the nature of their motion.

Findings

PN dynamics is non-chaotic in the specified cases

Explicit parametric solutions indicate integrability

Discrepancies with some numerical chaos results are discussed

Abstract

We formally show that the conservative second post-Newtonian (PN) accurate dynamics of spinning compact binaries moving in eccentric orbits, when spin effects are restricted to the leading order spin-orbit interaction cannot be chaotic for the following two distinct cases: (i) the binary consists of compact objects of arbitrary mass, where only one of them is spinning with an arbitrary spin and (ii) the binary consists of equal mass compact objects, having two arbitrary spins. We rest our arguments on the recent determination of PN accurate Keplerian-type parametric solutions to the above cases, indicating that the PN accurate dynamics is integrable in these two situations. We compare predictions of our case (i) with those from a numerical investigation of an equivalent scenario that observed chaos in the associated dynamics. We also present possible reasons for the discrepancies.