Holonomy, decomposability, and relativity1This paper was presented at the Theory CANADA 4 conference, held at Centre de recherches mathématiques, Montréal, Québec, Canada on 4–7 June 2008.

Abstract

We discuss the geometrical properties of spacetimes in the context of higher dimensional theories of gravity. If the spacetime admits a covariantly constant time-like vector, the spacetime is static and (1+10)-decomposable, where the 10-dimensional transverse space is Riemannian. The second class of solutions consists of spacetimes that admit a covariantly constant light-like vector and belong to the higher dimensional Kundt class of spacetimes. These spacetimes are genuinely Lorentzian and have many mathematical properties quite different from their Riemannian counterparts, which can lead to interesting and novel physics. This paper is a review of results published elsewhere (J. Brannlund, A. Coley, and S. Hervik. Class. Quantum Grav. 25, 195007 (2008)).