MG11 
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Symmetry factorization of Einstein equations with cosmological constant

We perform symmetry analysis of the Einstein equations with cosmological constant ?, admitting two commuting Killing vectors that are orthogonal to a foliation by 2-dimensional leaves. In case of ? = 0 the equations reduce to the well-understood Ernst equation; therefore we concentrate on the case ? ­ 0. As the main result, we obtained the factorization of these equations with respect to a maximal subgroup of codimension 1; this solves the problem of geometrical equivalence of solutions. We have also identified several geometrically motivated subcases when the equations reduce to ODEs.