Abstract. We study manifolds with Lorentzian signature and prove that all scalar curvature invariants of all orders vanish in a higher dimensional Lorentzian spacetime if and only if there exists an aligned non-expanding, non-twisting, geodesic null direction along which the Riemann tensor has negative boost order.

PACS numbers: 04.20.Jb, 02.40.−k

Print publication: Issue 23 (7 December 2004)
Received 5 September 2004
Published 16 November 2004