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- Title
On the geometrization of matter by exotic smoothness.
- Authors
Asselmeyer-Maluga, Torsten; Rosé, Helge
- Abstract
In this paper we discuss the question how matter may emerge from space. For that purpose we consider the smoothness structure of spacetime as underlying structure for a geometrical model of matter. For a large class of compact 4-manifolds, the elliptic surfaces, one is able to apply the knot surgery of Fintushel and Stern to change the smoothness structure. The influence of this surgery to the Einstein-Hilbert action is discussed. Using the Weierstrass representation, we are able to show that the knotted torus used in knot surgery is represented by a spinor fulfilling the Dirac equation and leading to a Dirac term in the Einstein-Hilbert action. For sufficient complicated links and knots, there are 'connecting tubes' (graph manifolds, torus bundles) which introduce an action term of a gauge field. Both terms are genuinely geometrical and characterized by the mean curvature of the components. We also discuss the gauge group of the theory to be U(1) × SU(2) × SU(3).
- Subjects
SMOOTHNESS of functions; GEOMETRIC analysis; SPACETIME; EINSTEIN field equations; GAUGE field theory; KNOT theory
- Publication
General Relativity & Gravitation, 2012, Vol 44, Issue 11, p2825
- ISSN
0001-7701
- Publication type
Article
- DOI
10.1007/s10714-012-1419-3