Abstract
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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.