A note on colliding-wave solutions with variable polarization (Q1576187)

Choosing an appropriate seed function (a general solution of the Laplace equation) the whole set of metric fields corresponding to the solution representing collisions between plane gravitational waves with variable polarization is found in a concise analytical form. The paper stresses mathematical results since the physical properties of the colliding wave solutions are essentially the same as in the literature. For illustration two simplest solutions for colliding plane waves with noncolinear polarization are derived corresponding to the Chandrasekhar-Xanthopoulos solution and the Nutku-Halil solution. Methods used in the present paper can be applied not only to the colliding wave solutions but also to obtain new cosmological solutions in vacuum having also two spacelike Killing vectors but different boundary conditions.