Spinning compact binary dynamics and chameleon orbits

TL;DR

This paper develops a detailed 2PN order model for spinning compact binary systems, deriving equations that incorporate spin effects and conservation laws, and demonstrates the existence of chameleon orbits where orbital parameters change from elliptic to hyperbolic.

Contribution

It provides a closed-form set of evolution equations for spinning binaries at 2PN order, including spin effects and a novel analysis of chameleon orbits in relativistic gravity.

Findings

Derived a compact system of differential equations for binary evolution.

Proved the preservation of constraints in the dynamical system.

Showed the existence of chameleon orbits with changing orbital characteristics.

Abstract

We analyse the conservative evolution of spinning compact binaries to second post-Newtonian (2PN) order accuracy, with leading order spin-orbit, spin-spin and mass quadrupole-monopole contributions included. As a main result we derive a closed system of first order differential equations in a compact form, for a set of dimensionless variables encompassing both orbital elements and spin angles. These evolutions are constrained by conservation laws holding at 2PN order. As required by the generic theory of constrained dynamical systems we perform a consistency check and prove that the constraints are preserved by the evolution. We apply the formalism to show the existence of chameleon orbits, whose local, orbital parameters evolve from elliptic (in the Newtonian sense) near pericenter, towards hyperbolic at large distances. This behavior is consistent with the picture that General Relativity predicts stronger gravity at short distances than Newtonian theory does.