  We study an even dimensional manifold with a pseudo-Riemannian metric with
arbitrary signature and arbitrary dimensions. We consider the Ricci flat
equations and present a procedure to construct solutions to some higher (even)
dimensional Ricci flat field equations from the four diemnsional Ricci flat
metrics. When the four dimensional Ricci flat geometry correponds to a
colliding gravitational vacuum spacetime our approach provides an exact
solution to the vacuum Einstein field equations for colliding graviational
plane waves in an (arbitrary) even dimensional spacetime. We give explicitly
higher dimensional Szekeres metrics and study their singularity behaviors.

General Relativity and Quantum Cosmology