Gravitational waves in vacuum spacetimes with cosmological constant. II. Deviation of geodesics and interpretation of nontwisting type N solutions

In a suitably chosen essentially unique frame tied to a given observer in a general spacetime, the equation of geodesic deviation can be decomposed in to a sum of terms describing specific effects: isotropic (background) motio ns associated with the cosmological constant, transverse motions correspond ing to the effects of gravitational waves, longitudinal motions and Coulomb -type effects. Conditions under which the frame is parallelly transported a long a geodesic are discussed. Suitable coordinates are introduced and an e xplicit coordinate form of the frame is determined for spacetimes admitting a nontwisting null congruence. Specific properties of all nontwisting type N vacuum solutions with cosmological constant Lambda (nonexpanding Kundt c lass and expanding Robinson-Trautman class) are then analyzed. It is demons trated that these spacetimes can be understood as exact transverse gravitat ional waves of two polarization modes "+" and "x," shifted by pi/4, which p ropagate "on" Minkowski, de Sitter or anti-de Sitter backgrounds. It is als o shown that the solutions with Lambda > 0 may serve as exact demonstration s of the cosmic "no-hair" conjecture in radiative spacetimes with no symmet ry. (C) 1999 American Institute of Physics. [S0022-2488(99)00609-X].