Impulsive gravitational waves generated by null particles in de Sitter and anti–de Sitter backgrounds

By boosting the metric of the Schwarzschild–de Sitter and Schwarzschild–anti-de Sitter space-times in the ultrarelativistic limit as the mass parameter vanishes, impulsive gravitational waves are obtained in backgrounds with a nonzero cosmological constant. We determine the geometry of these impulsive wave surfaces using various coordinate charts. In the de Sitter background they are spheres containing two null particles located at the poles. In the anti–de Sitter background they are hyperboloidal surfaces of constant negative curvature containing a single null particle on the axis of symmetry. The global structure and conformal diagrams for the complete manifolds are also determined.