Maths HEP Lunchtime Seminars: On the Newman-Penrose formalism in higher dimensions: Robinson-Trautman and Kerr-Schild spacetimes
12 December 2008 13:00 in CM221
The study of geometric optics has played an important role in the construction and classification of exact solutions of Einstein's equations in D=4 dimensions. A remarkable connection with the Petrov classification is provided by the Goldberg-Sachs theorem ("a vacuum metric is algebraically special iff it contains a shearfree geodesic null congruence"). In the past few years, possible extensions of these concepts to higher dimensions have been investigated. For instance, it has been shown that the Goldberg-Sachs theorem is "violated" in many ways when D>4 (e.g. by Myers-Perry black holes), and some consequences of the Bianchi and Ricci identities have been studied. After an introductory review, we will describe the D>4 Robinson-Trautman and Kerr-Schild classes of spacetimes to exemplify some of these ideas.