Type N solutions of the vacuum scalar-tensor field equations

Abstract

All solutions of the vacuum relativistic scalar-tensor field equations Rμυ=−φ,μφ,υ are given in the case where the Weyl tensor is of Petrov-Penrose type N. These eight solutions are listed according to the Petrov-Plebanski classification of their trace-free Ricci tensor components and belong to the three classes[T−3S][1−1] (R,N), [3T−S][1−1](R,N) and [4N][2](O,N).