Professor Wheeler and the crack of doom: Closed cosmologies in the 5-d Kaluza-Klein theory

Journal Article · Sat Mar 01 00:00:00 EST 1986 · Found. Phys.; (United States)

DOI:https://doi.org/10.1007/BF01889474· OSTI ID:5875018

Matzner, R A; Mezzacappa, A

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.

• Research Organization: Center for Reltivity and Physics Department, The University of Texas at Austin, Austin, Texas 78712
• OSTI ID: 5875018
• Journal Information: Found. Phys.; (United States), Vol. 16:3
• Country of Publication: United States
• Language: English

Related Subjects

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