The surfing effect in the interaction of electromagnetic and gravitational waves. Limits on the speed of gravitational waves

TL;DR

This paper explores how electromagnetic waves interact with gravitational waves, introducing the surfing effect, and uses it to set upper limits on deviations of gravitational wave speed from light speed based on upcoming interferometry precision.

Contribution

It introduces the surfing effect in electromagnetic-gravitational wave interaction and derives constraints on gravitational wave velocity deviations using high-precision interferometry.

Findings

Surfing effect causes observable consequences if gravitational wave speed differs from light speed.

Upcoming interferometry can constrain velocity deviation parameter to about 2% for certain energy densities.

Limits on gravitational wave speed deviation depend on gravitational wave energy density parameter.

Abstract

In the current work we investigate the propagation of electromagnetic waves in the field of gravitational waves. Starting with simple case of an electromagnetic wave travelling in the field of a plane monochromatic gravitational wave we introduce the concept of surfing effect and analyze its physical consequences. We then generalize these results to an arbitrary gravitational wave field. We show that, due to the transverse nature of gravitational waves, the surfing effect leads to significant observable consequences only if the velocity of gravitational waves deviates from speed of light. This fact can help to place an upper limit on the deviation of gravitational wave velocity from speed of light. The micro-arcsecond resolution promised by the upcoming precision interferometry experiments allow to place stringent upper limits on $\epsilon = (v_{gw}-c)/c$ as a function of the energy density parameter for gravitational waves $\Omega_{gw}$. For $\Omega_{gw} \approx 10^{-10}$ this limit amounts to $\epsilon\lesssim 2\cdot 10^{-2}$.