Article
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Modeling Spacetime as a Branched Covering Space over 2-Knots
Version 1
: Received: 25 July 2019 / Approved: 30 July 2019 / Online: 30 July 2019 (15:09:44 CEST)
How to cite: Duston, C. Modeling Spacetime as a Branched Covering Space over 2-Knots. Preprints 2019, 2019070342. https://doi.org/10.20944/preprints201907.0342.v1 Duston, C. Modeling Spacetime as a Branched Covering Space over 2-Knots. Preprints 2019, 2019070342. https://doi.org/10.20944/preprints201907.0342.v1
Abstract
In this paper we review a proposal to represent the geometric degrees of freedom of the gravitational field as a branched covering space, and introduce a new application of this in which the branch loci are 1- or 2-knots. This allows one to construct arbitrary smooth, closed 3- and 4-manifolds with enough geometric and topological information to write down a partition function and calculate statistical quantities in the thermodynamic limit. Further, we find clear evidence for a dimensional reduction of the spacetime geometry from four to two. As an example, we choose a family of smooth 4-manifolds presented in this way, and calculate the entropy of the system.
Keywords
general relativity; geometry; topology; branched covering space; exotic smooth structure; knot theory
Subject
Physical Sciences, Thermodynamics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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