17 Aug 2012; IMS (UiTø), room U1=A228. 15:15-16:30.

Vladimir Matveev (Friedrich-Schiller-Universität Jena, Germany)

“(Non)existence of Killing tensors for Zipoy-Vorhees metric”

Zipoy-Voorhees metric is a Ricci flat metric of Lorenz signature with two commuting Killing vector fields, so that it is a stationary axially-symmetric vacuum solution of the Einstein equation. This metric has a real parameter δ, and for its values 0 and 1 the metric is Minkowsky and Schwarzschild respectively. Of course, the geodesic flow for these two metrics is Liouville integrable. It was conjectured by physicists, on the basis of observations, that integrability is preserved for other parameters δ.

In a joint paper with B.Kruglikov, using the geometric theory of differential equations, we proved that for δ=2 this is not the case. I will describe this and some other recent results about indication of (non)integrability.