Redshift Fluctuations arising from Gravitational Waves

Abstract

IT is well known that when light travels through a gravitational field, the field acts like a refracting medium. Even though space may be empty in the sense that the components of the Ricci tensor vanish, we still expect an effect on the propagation of light as suggested by Maxwell's equations where F_μv is the electromagnetic field tensor and R_μvαβ is the Riemann–Christoffel curvature tensor¹. If the space between a source of photons and an observer is filled with gravitational radiation, we then expect fluctuations in the appearance of the source analogous to the twinkling of starlight as seen through the Earth's atmosphere. Changes in the apparent luminosity and position of a source due to gravitational waves have been examined in the geometrical optics limit by Zipoy². Here I shall concern myself with fluctuations in the redshift.