Gravitational sources induced by exotic smoothness

Abstract

In this paper we construct a coordinate atlas in an exotic ${\mathbb{R}}^4$ using Bizaca's construction. The main source for such an atlas is the handle body decomposition of a Casson handle, which of course is an infinite, but periodic, process. The immersion of the end-periodic manifold into ${\mathbb{R}}^4$ is directly related to the exoticness of the ${\mathbb{R}}^4$ and also gives rise naturally to a spinor field. Thus we obtain the interesting result that the simplest exotic ${\mathbb{R}}^4$ generates an extra spinor field by exoticness.

17 pages, 8 figures, 5 appendices

References in corpus (2)

• Corks, Plugs and exotic structures
• Action and Hamiltonians in higher dimensional general relativity: First order framework