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

Abstract

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.

Authors:
;
Publication Date:
Research Org.:
Center for Reltivity and Physics Department, The University of Texas at Austin, Austin, Texas 78712
OSTI Identifier:
5875018
Resource Type:
Journal Article
Journal Name:
Found. Phys.; (United States)
Additional Journal Information:
Journal Volume: 16:3
Country of Publication:
United States
Language:
English
Subject:
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

Citation Formats

Matzner, R A, and Mezzacappa, A. Professor Wheeler and the crack of doom: Closed cosmologies in the 5-d Kaluza-Klein theory. United States: N. p., 1986. Web. doi:10.1007/BF01889474.
Matzner, R A, & Mezzacappa, A. Professor Wheeler and the crack of doom: Closed cosmologies in the 5-d Kaluza-Klein theory. United States. https://doi.org/10.1007/BF01889474
Matzner, R A, and Mezzacappa, A. 1986. "Professor Wheeler and the crack of doom: Closed cosmologies in the 5-d Kaluza-Klein theory". United States. https://doi.org/10.1007/BF01889474.
@article{osti_5875018,
title = {Professor Wheeler and the crack of doom: Closed cosmologies in the 5-d Kaluza-Klein theory},
author = {Matzner, R A and Mezzacappa, A},
abstractNote = {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.},
doi = {10.1007/BF01889474},
url = {https://www.osti.gov/biblio/5875018}, journal = {Found. Phys.; (United States)},
number = ,
volume = 16:3,
place = {United States},
year = {Sat Mar 01 00:00:00 EST 1986},
month = {Sat Mar 01 00:00:00 EST 1986}
}