A special class of Petrov type D vacuum space-times in dimension five

Alfonso García-Parrado Gómez-Lobo

In this work we study a special class of type D solutions of the Einstein vacuum equations in dimension five which is characterised by the existence of an invariant space-like congruence. The main tool used in our work is an generalisation of the G.H.P. formalism used in dimension four to the present case of dimension five. We discuss a number of invariant properties of these solutions, such as the existence of Killing vectors, the Karlhede bound or the presence of "global conserved scalar quantities" (mass, angular momentum, etc). We indicate how our techniques could be used in the analysis of more general vacuum type D, five-dimensional solutions.

Work done in collaboration with Dr. Lode Wylleman.