Gravitational sources induced by exotic smoothness

Details Gravitational sources induced by exotic smoothness Gravitational sources induced by exotic smoothness

2011-01-17

arxiv.org/abs/1101.3168v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

17 pages, 8 figures, 5 appendices

Scientific paper

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.

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