• DOI:10.1088/0264-9381/31/22/225006
• Corpus ID: 119241733

The Geroch group in Einstein spaces

@article{Leigh2014TheGG,
  title={The Geroch group in Einstein spaces},
  author={Robert G. Leigh and Anastasios C. Petkou and P Marios Petropoulos and Prasanta Kumar Tripathy},
  journal={Classical and Quantum Gravity},
  year={2014},
  volume={31}
}

• R. Leigh, A. Petkou, +1 author P. Tripathy
• Published 25 March 2014
• Physics, Mathematics
• Classical and Quantum Gravity

Gerochʼs 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 × S 2 ?> . The cosmological constant appears in this framework as a constant of motion and transforms under SL ( 2 , R ) ?> .