Surfing effect in the interaction of electromagnetic and gravitational waves: Limits on the speed of gravitational waves

Abstract

In the current work we investigate the propagation of electromagnetic waves in the field of gravitational waves. Starting with the simple case of an electromagnetic wave traveling in the field of a plane monochromatic gravitational wave, we introduce the concept of the 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 the speed of light. This fact can help to place an upper limit on the deviation of gravitational wave velocity from the speed of light. The microarcsecond resolution promised by the upcoming precision interferometry experiments allow one to place stringent upper limits on $ϵ=({v}_{\mathrm{gw}}\ensuremath{-}c)/c$ as a function of the energy density parameter for gravitational waves ${\ensuremath{\Omega}}_{\mathrm{gw}}$. For ${\ensuremath{\Omega}}_{\mathrm{gw}}\ensuremath{\approx}{10}^{\ensuremath{-}10}$ this limit amounts to $ϵ\ensuremath{\lesssim}2\ifmmode\cdot\else\textperiodcentered\fi{}{10}^{\ensuremath{-}2}$.