Boosting gravitational waves: a review of kinematic effects on amplitude, polarization, frequency and energy density

TL;DR

This review discusses how kinematic effects like source and observer motion influence gravitational wave amplitude, polarization, frequency, and energy density, with implications for astrophysical observations and cosmology.

Contribution

It provides a comprehensive analysis of fully non-linear kinematic effects on gravitational waves, including amplitude amplification, polarization rotation, and intensity transformation.

Findings

Amplitude is Doppler-boosted by source motion.

Polarization phase shifts due to boosts.

Intensity transforms similarly under source or observer motion.

Abstract

We review the kinematic effects on a gravitational wave due to either a peculiar motion of the astrophysical source emitting it or a local motion of the observer. Working in the context of general relativity, we show at fully non-linear order in velocity, that the amplitude of the wave is amplified by the Doppler factor in the case in which the source moves with respect to a reference frame, while it is invariant if the observer moves (with respect to a reference observer). However, the observed specific intensity transforms in the same way under a boost of the source or of the observer. We also show at fully non-linear order that under a boost (of either source or observer), the polarization tensor is rotated in the same way the wave direction is rotated by aberration, such that the only net effect of a boost on polarization is to change the phase of the helicity components. We apply these results to a wave emitted by a binary system of compact objects in the cosmological context.