Curvature invariants in type-III spacetimes

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.

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

References in corpus (1)

• Two loop and all loop finite 4-metrics

Cited by in corpus (9)

• All spacetimes with vanishing curvature invariants
• Vanishing Scalar Invariant Spacetimes in Higher Dimensions
• Algebraic classification of higher dimensional spacetimes based on null alignment
• Metrics With Vanishing Quantum Corrections
• A Class of Exact Classical Solutions to String Theory
• Type III and N Einstein spacetimes in higher dimensions: general properties
• On higher dimensional Einstein spacetimes with a warped extra dimension
• What happens to Petrov classification on horizons of axisymmetric dirty black holes
• Note on Invariants of the Weyl Tensor