The Geroch group in Einstein spaces

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

Research output: Contribution to journalArticlepeer-review


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).

Original languageEnglish (US)
Article number225006
JournalClassical and Quantum Gravity
Issue number22
StatePublished - Nov 21 2014


  • Geroch group
  • exact solutions of Einsteins equations
  • gravity

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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