Curvature invariants in type-III spacetimes

Details Curvature invariants in type-III spacetimes Curvature invariants in type-III spacetimes

1999-06-30

arxiv.org/abs/gr-qc/9906121v2

Class.Quant.Grav.16:3321-3326,1999

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

1 reference added, typos corrected, accepted for publication in Clas. Quantum Grav

Scientific paper

10.1088/0264-9381/16/10/321

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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