Refraction index analysis of light propagation in a colliding   gravitational wave spacetime
  The optical medium analogy of a given spacetime was developed decades ago and has since then been widely applied to different gravitational contexts. Here we consider the case of a colliding gravitational wave spacetime, generalizing previous results concerning single gravitational pulses. Given the complexity of the nonlinear interaction of two gravitational waves in the framework of general relativity, typically leading to the formation of either horizons or singularities, the optical medium analogy proves helpful to simply capture some interesting effects of photon propagation. 
Donato Bini, Andrea Geralico, Maria Haney
gr-qc