Abstract. A higher dimensional frame formalism is developed in order to study implications of the Bianchi identities for the Weyl tensor in vacuum spacetimes of the algebraic types III and N in arbitrary dimension n. It follows that the principal null congruence is geodesic and expands isotropically in two dimensions and does not expand in n − 4 spacelike dimensions or does not expand at all. It is shown that the existence of such principal geodesic null congruence in vacuum (together with an additional condition on twist) implies an algebraically special spacetime. We also use the Myers–Perry metric as an explicit example of a vacuum type D spacetime to show that principal geodesic null congruences in vacuum type D spacetimes do not share this property.

PACS number: 04.50.-h

A corrigendum for this article has been published in 2007 Class. Quantum Grav. 24 1691

Print publication: Issue 12 (21 June 2004)
Received 28 November 2003
Published 18 May 2004