# Constructing Gravitational Waves from Generic Spin-Precessing Compact Binary Inspirals

## TL;DR

This paper develops the first closed-form frequency-domain gravitational waveforms for generic spin-precessing compact binary inspirals, enabling more accurate and computationally efficient detection and analysis of gravitational waves from such systems.

## Contribution

It introduces a novel method to construct analytic frequency-domain waveforms for precessing binaries, combining post-Newtonian precession equations with shifted uniform asymptotics.

## Key findings

- Waveforms are accurate for 99.2% of configurations at SNR 10.
- Waveforms are suitable for unbiased parameter estimation.
- Method reduces computational cost for gravitational wave data analysis.

## Abstract

The coalescence of compact objects is one of the most promising sources of gravitational waves for ground-based interferometric detectors, such as advanced LIGO and Virgo. Generically, com- pact objects in binaries are expected to be spinning with spin angular momenta misaligned with the orbital angular momentum, causing the orbital plane to precess. This precession adds rich structure to the gravitational waves, introducing such complexity that an analytic closed-form description has been unavailable until now. We here construct the first closed-form frequency- domain gravitational waveforms that are valid for generic spin-precessing quasicircular compact binary inspirals. We first construct time-domain gravitational waves by solving the post-Newtonian precession equations of motion with radiation reaction through multiple scale analysis. We then Fourier transform these time-domain waveforms with the method of shifted uniform asymptotics to obtain closed-form expressions for frequency-domain waveforms. We study the accuracy of these analytic, frequency-domain waveforms relative to waveforms obtained by numerically evolving the post-Newtonian equations of motion and find that they are suitable for unbiased parameter estimation for 99.2%(94.6%) of the binary configurations we studied at a signal-to-noise ratio of 10(25). These new frequency-domain waveforms could be used for detection and parameter estimation studies due to their accuracy and low computational cost.