Stationary ``Noncanonical'' Solutions of the Einstein Vacuum Field Equations

Abstract

The complete set of nonflat normal-hyperbolic solutions of the Einstein vacuum field equations is obtained for the metric tensor defined by the quadratic differential form ds2 = α du2 − 2γ du dv − β dv2 − eφ(dx2 + dz2) subject to the condition that αβ + γ2 is constant. These solutions are characterized by the existence of a null hypersurface-orthogonal Killing vector, which is also a four-fold degenerate Debever vector with vanishing covariant derivative, and therefore are a special case of the class of plane-fronted gravitational waves.