Professor Wheeler and the crack of doom: Closed cosmologies in the 5-d Kaluza-Klein theory
We study the classical and the quantum structures of certain 5-d Kaluza-Klein cosmologies. These models were chosen because their 4-d restriction is a closed, radiation-dominated, homogeneous, isotropic cosmology in the usual sense. The extra (field) dimension is taken to be a circle. In these models the solution starts from a 5-d curvature singularity with infinite circumference for the circle and zero volume for the 3-space. It evolves in finite proper time to a solution with zero dimension for the extra field direction. In the 5-vacuum case this is not a curvature singularity, but is a singularity of the congruence describing the physics, and in particular, the solution cannot causally be extended to the future of this point. In the 5-vacuum case this event coincides with the maximum of expansion of the 5-space. In the 5-dust cases, this point is a real 5-d curvature singularity. By adjustment it can be made to occur before or after the maximum of 3-expansion. The solution stops at that instant, but the 4-cosmology reveals no pathology up to the crack of doom. The quantum behavior is identical in these respects to the classical one.
- Publication Date:
- OSTI Identifier:
- Resource Type:
- Journal Article
- Resource Relation:
- Journal Name: Found. Phys.; (United States); Journal Volume: 16:3
- Research Org:
- Center for Reltivity and Physics Department, The University of Texas at Austin, Austin, Texas 78712
- Country of Publication:
- United States
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COSMOLOGICAL MODELS; KALUZA-KLEIN THEORY; EINSTEIN FIELD EQUATIONS; HAMILTONIANS; SINGULARITY; EQUATIONS; FIELD EQUATIONS; FIELD THEORIES; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; QUANTUM OPERATORS; UNIFIED-FIELD THEORIES 640106* -- Astrophysics & Cosmology-- Cosmology
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