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Curvature invariants in type-III spacetimes

V. Pravda
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Abstract

The results of paper [1] are generalized for vacuum type-III solutions with, in general, a non-vanishing cosmological constant Lambda. It is shown that all curvature invariants containing derivatives of the Weyl tensor vanish if a type-III spacetime admits a non-expanding and non-twisting null geodesic congruence. A non-vanishing curvature invariant containing first derivatives of the Weyl tensor is found in the case of type-III spacetime with expansion or twist.

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V. Pravda. 1999-08-17. Curvature invariants in type-III spacetimes. https://doi.org/10.1088/0264-9381%2F16%2F10%2F321

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