On the geometrization of matter by exotic smoothness - General Relativity and Quantum CosmologyReport as inadecuate




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Abstract: In this paper we discuss the question how matter may emerge from space. Forthat purpose we consider the smoothness structure of spacetime as underlyingstructure for a geometrical model of matter. For a large class of compact4-manifolds, the elliptic surfaces, one is able to apply the knot surgery ofFintushel and Stern to change the smoothness structure. The influence of thissurgery to the Einstein-Hilbert action is discussed. Using the Weierstrassrepresentation, we are able to show that the knotted torus used in knot surgeryis represented by a spinor fulfilling the Dirac equation and leading to amass-less Dirac term in the Einstein-Hilbert action. For sufficient complicatedlinks and knots, there are -connecting tubes- graph manifolds, torus bundleswhich introduce an action term of a gauge field. Both terms are genuinelygeometrical and characterized by the mean curvature of the components. We alsodiscuss the gauge group of the theory to be U1xSU2xSU3.



Author: Torsten Asselmeyer-Maluga, Helge Rose

Source: https://arxiv.org/







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