Influence of gravitational waves upon light. Part I. Null geodesics, radar distance and frequency shift

TL;DR

This paper analyzes how linearized gravitational waves affect light's path, frequency, and radar distance in Minkowski spacetime, providing explicit calculations and clarifications on gravitational wave detection via interferometry.

Contribution

It offers explicit calculations of null geodesics, radar distance, and frequency shifts caused by gravitational waves, clarifying detection mechanisms in a linearized gravity context.

Findings

Explicit null geodesic solutions between observers

Quantitative relations for radar distance and frequency shift

Explanation of interferometric detection despite arm stretching

Abstract

We explore different facets of the action of linearized gravitational waves in Minkowski spacetime background upon light, under the electromagnetic geometrical optics limit, covering the main aspects: light trajectory perturbations, radar distance and light frequency shift. For this purpose, we consider observers comoving with the transverse traceless gauge coordinates. We compute the parametrized null geodesics exchanged between two of these observers, presenting explicitly the constants of motion as functions of observables, determining therefrom both the radar distance between the observers and the electromagnetic round-trip frequency shift caused by the gravitational wave. Also, a comparison is made between these results and what one would obtain by using a frequently adopted hybrid model in which the spatial trajectory of light is unchanged. Finally, we revisit and provide an explanation, resorting to the constancy of the phase along a light ray, to the fundamental puzzling question of how one is able to detect gravitational waves by means of interferometry if both light wavelength and detector arms are stretched.