Non-expanding impulsive gravitational waves

Abstract

We investigate a class of impulsive gravitational waves which propagate either in Minkowski or in the (anti-) de Sitter background. These waves are constructed as impulsive members of the Kundt class of non-twisting, non-expanding type-N solutions of vacuum Einstein equations with a cosmological constant . We show that the only non-trivial waves of this type in Minkowski spacetime are impulsive pp-waves. For we demonstrate that the canonical subclasses of , which are invariantly different for smooth profiles, are all locally equivalent for impulsive profiles. Also, we present a coordinate system for these impulsive solutions which is explicitly continuous.