The Frenet-Serret formalism and black holes in higher dimensions

Abstract

The Frenet-Serret formalism is applied to the study of Killing trajectories in higher dimensions (five and six). The curvature and the higher torsions are expressed in terms of an effective field strength Fab and their mutual relations established by the use of the Cayley-Hamilton theorem. This is used to show that the surface on which the timelike Killing vector becomes null is a null surface only if the 'rotation' is also null on it.