Professor wheeler and the crack of doom: Closed cosmologies in the 5-d Kaluza-Klein theory
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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 revealsno pathology up to the crack of doom. The quantum behavior is identical in these respects to the classical one.
KeywordsProper Time Field Direction Usual Sense Curvature Singularity Quantum Structure
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