Symmetry reduced Einstein gravity and generalized σ and chiral models

Abhay Ashtekar, Viqar Husain

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Certain features associated with the symmetry reduction of the vacuum Einstein equations by two commuting, spacelike Killing vector fields are studied. In particular, the discussion encompasses the equations for the Gowdy T3 cosmology and cylindrical gravitational waves. We first point out a relation between the SL(2,R) (or SO(3)) σ and principal chiral models, and then show that the reduced Einstein equations can be obtained from a dimensional reduction of the standard SL(2,R) σ-model in three dimensions. The reduced equations can also be derived from the action of a 'generalized' two dimensional SL(2,R) σ-model with a time dependent constraint. We give a Hamiltonian formulation of this action, and show that the Hamiltonian evolution equations for certain phase space variables are those of a certain generalization of the principal chiral model. Using these Hamiltonian equations, we give a prescription for obtaining an infinite set of constants of motion explicitly as functionals of the spacetime metric variables.

Original languageEnglish (US)
Pages (from-to)549-566
Number of pages18
JournalInternational Journal of Modern Physics D
Issue number4
StatePublished - Aug 1998

All Science Journal Classification (ASJC) codes

  • Mathematical Physics
  • Astronomy and Astrophysics
  • Space and Planetary Science


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