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arXiv · 1403.6511

The Geroch group in Einstein spaces

Robert G. Leigh·Anastasios C. Petkou·P. Marios Petropoulos·Prasanta K. Tripathy
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Abstract

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 $SL(2,\mathbb{R})$ 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 $\mathbb{R}\times \mathcal{S}_2$. The cosmological constant appears in this framework as a constant of motion and transforms under $SL(2,\mathbb{R})$.

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Robert G. Leigh, Anastasios C. Petkou, P. Marios Petropoulos, Prasanta K. Tripathy. 2014-03-25. The Geroch group in Einstein spaces. https://doi.org/10.1088/0264-9381/31/22/225006

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