Gravitational waves in vacuum spacetimes with cosmological constant. I. Classification and geometrical properties of nontwisting type N solutions

All nontwisting Petrov-type N solutions of vacuum Einstein field equations with cosmological constant Lambda are summarized. They are shown to belong either to the nonexpanding Kundt class or to the expanding Robinson-Trautma n class. Invariant subclasses of each class are defined and the correspondi ng metrics are given explicitly in suitable canonical coordinates. Relation s between the subclasses and their geometrical properties are analyzed. In the subsequent paper these solutions are interpreted as exact gravitational waves propagating in de Sitter or anti-de Sitter spacetimes. (C) 1999 Amer ican Institute of Physics. [S0022-2488(99)00509-5].