Role of the initial data in the problem of collision of plane gravitational waves with collinear polarization

Abstract

The work deals with analysis of a gravitational field near a focusing surface in the interaction region of colliding plane waves with collinear polarization. The profiles of the initial waves are supposed to be arbitrary, satisfying only some smoothness conditions behind their fronts. The asymptotic expansions of the metric coefficients, optical scalars, and tetrad components of the curvature tensor near the focusing surface are derived by a direct analysis of the integral form of the solution of the problem obtained long ago by Szekeres. The approach allows us to obtain rigorously more detailed asymptotic representations of the functions under consideration. The dependence of singularity terms on the functions characterizing the initial waves is explored. Conditions for absence of a true singularity on the focusing surface are discussed.