The Geroch group in Einstein spaces

Geroch;s solution-generating method is extended to the case of Einstein spaces, which possess a Killing vector and are thus asymptotically (locally) (anti) de Sitter. This includes the reduction to a three-dimensional coset space, the description of the dynamics in terms of a sigma-model and its transformation properties under the SL (2, ℝ) group, and the reconstruction of new four-dimensional Einstein spaces. The detailed analysis of the space of solutions is performed using the Hamilton-Jacobi method in the instance where the three-dimensional coset space is conformal to ℝ × S₂. The cosmological constant appears in this framework as a constant of motion and transforms under SL (2, ℝ).