Colliding gravitational waves in expanding cosmologies

Abstract

We discuss the singularity behavior and causal structure of expanding vacuum plane-symmetric cosmologies containing colliding gravitational waves. Penrose's theorem excluding global Cauchy hypersurfaces in plane-wave spacetimes does not hold for our expanding cosmologies. The singularity in our solutions occurs in the past and can be identified with the big-bang singularity. Analytical estimates based on a Green's-function analysis near the collision provide an explicit example which is verified by numerical computation.