Spinning binary waveforms via PN expansion: Equal-mass case

TL;DR

This paper derives fully analytical gravitational waveform expressions for equal-mass spinning binary inspirals using post-Newtonian approximation, simplifying complex equations through symmetry, and including spin-orbit effects up to 1.5 PN order.

Contribution

It provides the first complete analytical solutions for equal-mass spinning binary waveforms up to 1.5 PN order, leveraging symmetry to simplify the equations.

Findings

Analytical waveform expressions derived for equal-mass spinning binaries.

Inclusion of spin-orbit interactions up to 1.5 PN order.

Simplification of equations due to symmetry in equal-mass systems.

Abstract

Complete expressions of time-domain gravitational waveforms for spinning binary inspirals via the post-Newtonian (PN) approximation would require determination of the phase, amplitude, inclination angle, precession phase and spin vectors as well as the knowledge of the order coefficients for the PN expansion terms. These quantities are determined by solving simultaneously the spin-precession equations, the evolution equation for the Newtonian angular momentum, and the equation for the orbital frequency. For the spinning binaries with equal masses, determination of these quantities can be done fully analytically, by taking advantage of the equal mass symmetry, therefore by simplifying those equations to solve. We provide the analytical results through 1.5 PN order which includes spin-orbit interactions.