Deriving analytic solutions for compact binary inspirals without recourse to adiabatic approximations

TL;DR

This paper introduces a dynamical renormalization group approach to derive analytic solutions for compact binary inspirals, avoiding orbit averaging and systematically including higher-order corrections for improved accuracy over long times.

Contribution

It presents a novel application of the renormalization group formalism to obtain closed-form, long-time solutions for binary inspirals without relying on adiabatic approximations.

Findings

Derived second-order corrections to radiation reaction force.

Systematically included post-Newtonian corrections.

Achieved long-time accurate analytic solutions without orbit averaging.

Abstract

We utilize the dynamical renormalization group formalism to calculate the real space trajectory of a compact binary inspiral for long times via a systematic resummation of secularly growing terms. This method generates closed form solutions without orbit averaging, and the accuracy can be systematically improved. The expansion parameter is $v^5 \nu \Omega(t-t_0)$ where $t_0$ is the initial time, $t$ is the time elapsed, and $\Omega$ and $v$ are the angular orbital frequency and initial speed, respectively, and $\nu$ is the binary's symmetric mass ratio. We demonstrate how to apply the renormalization group method to resum solutions beyond leading order in two ways. First, we calculate the second order corrections of the leading radiation reaction force, which involves highly non-trivial checks of the formalism (i.e. its renormalizability). Second, we show how to systematically include post-Newtonian corrections to the radiation reaction force. By avoiding orbit averaging we gain predictive power and eliminate ambiguities in the initial conditions. Finally, we discuss how this methodology can be used to find analytic solutions to the spin equations of motion that are valid over long times.