Plane gravitational waves

Starting with plane gravitational waves of arbitrary profile as solutions of Einstein’s vacuum field equations in the linear approximation a sequence of gauge transformations results in a metric tensor which is an exact solution of the vacuum field equations. The Khan–Penrose solution of Einstein’s vacuum field equations describing the gravitational field following the head-on collision of plane gravitational impulsive waves is derived. The head-on collision of electromagnetic and gravitational shock waves is discussed with the latter collision resulting in the appearance of ‘dark energy’ in the gravitational field following the collision. High-frequency plane and spherical fronted gravitational waves are also discussed.