Abstract

We systematically review the solutions of the vacuum Einstein equations for the axially symmetric stationary case which are harmonic maps. In particular, we show that the interesting part of the Kerr solution is a composition of a harmonic map intoH12 with a totally geodesic map fromH12 into SS(1,1). We also point out, relying on Sanchez' results, that there is an analogous structure for the Lorentz-domain cases involving cylindrical gravitational waves and colliding plane waves.

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