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

1 May 1969

journal article
research article
Published by AIP Publishing in Journal of Mathematical Physics

Vol. 10 (5) , 953-956
https://doi.org/10.1063/1.1664926

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 − e^φ(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.

Keywords

This publication has 2 references indexed in Scilit:

Gravitational waves in general relativity. VI. The outgoing radiation condition
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1961
On Riemann Spaces Conformal to Euclidean Space
Proceedings of the National Academy of Sciences, 1923