In this talk we briefly review the Geroch method of generating new solutions from given Ricci flat metrics admitting a Killing vector. We will then discuss the generalization of this method for Einstein metrics admitting a Killing vector. The description is given in terms of a non-linear sigma model in the three dimensional coset space (formed by the orbits invariant under the Killing vector). We will discuss the integrability of this model for a simple case when the coset space is conformal to R × M2.
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