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

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

2003-07-31

arxiv.org/abs/gr-qc/0307121v2

Class.Quant.Grav. 20 (2003) 5309-5319

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

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

Scientific paper

10.1088/0264-9381/20/24/005

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.

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