The structure of spherically symmetric static solutions is quite well understood and I will discuss a number of their features since they indicate what features can be expected of axisymmetric solutions. Existence of axially symmetric stationary solutions that are perturbed off from spherically symmetric Newtonian solutions have been obtained analytically whereas solutions far from spherically symmetric have only been
constructed numerically. I will discuss the properties of the latter. In particular, two different sequences of toroidal solutions which contain ergoregions will be described in detail. These solutions either approach an extreme Kerr black hole or they have the property that the geometry becomes conical in the limit and such solutions may provide models of cosmic strings.
Håkan Andréasson (Gothenburg): On the existence and structure of stationary solutions of the Einstein‐Vlasov system
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