7 research outputs found
On the geometrization of matter by exotic smoothness
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
mass-less 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)xSU(2)xSU(3).Comment: 30 pages, 3 figures, svjour style, complete reworking now using
Fintushel-Stern knot surgery of elliptic surfaces, discussion of Lorentz
metric and global hyperbolicity for exotic 4-manifolds added, final version
for publication in Gen. Rel. Grav, small typos errors fixe