Reduction of the Einstein-Maxwell and Einstein-Maxwell-Higgs equations for cosmological space-times with space - like U(1) isometry groups
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Abstract: (IOP)
The author considers electrovacuum spacetimes with spacelike U(1) isometry groups which are defined on manifolds of the form R*Bn where Bn is an arbitrary S1-bundle over the 2-sphere. He reduces the Einstein-Maxwell equations for this problem to a system of pure 'harmonic map' evolution equations defined on the base manifold R*S2 by solving an elliptic system of 'constraint' equations for the non-propagating dependent variables. He also shows how an action of SU(2,1) can sometimes be applied to the fields defined on the base manifold to transform solutions corresponding to one bundle to solutions corresponding to an inequivalent bundle. He also reduces the Einstein-Maxwell-Higgs equations with a spacelike U(1) isometry group defined on the bundle R*T3 to R*T2. The reduced field equations provide a natural framework for the study of colliding, self-gravitating parallel (or antiparallel) cosmic strings in the cosmological context of a closed universe.- Einstein-Maxwell equation
- space-time
- fibre bundle
- electromagnetic field
- field theory: constraint
- Hopf map
- field theory: integrability
- coset space
- cohomology
- topology
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