Mappings of empty space-times leaving the curvature tensor invariant

Details Mappings of empty space-times leaving the curvature tensor invariant Mappings of empty space-times leaving the curvature tensor invariant

Jan 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982gregr..14....5c&link_type=abstract

General Relativity and Gravitation, Volume 14, Issue 1, pp.5-15

Computer Science

12

Scientific paper

It is shown that if in some local coordinate system the componentsR i jkl of the curvature tensor of an empty space-time are known, then, provided the space-time is not of Petrov typeN with hypersurface orthogonal geodesic rays, the components of the metric tensor are uniquely determined up to a trivial constant scaling factor. The Petrov type-N empty space-times with hypersurface orthogonal geodesic rays are investigated. The most general mappings leaving the curvature tensorR i jkl invariant are found for each class of these space-times.

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