Vacuum spacetimes with a spacelike, hypersurface-orthogonal Killing vector: reduced equations in a canonical frame

Abstract

The Newman-Penrose equations for spacetimes having one spacelike Killing vector are reduced -- in a geometrically defined "canonical frame'' -- to a minimal set, and its differential structure is studied. Expressions for the frame vectors in an arbitrary coordinate basis are given, and coordinate-independent choices of the metric functions are suggested which make the components of the Ricci tensor in the direction of the Killing vector vanish.

13 pages, no figures, LaTeX, to be published in Class. Quantum Gravity; v2: added/rephrased content, corrected typos, changed 1 reference