On 4-dimensional Lorentz-structures, Dark energy and Exotic smoothness

Details On 4-dimensional Lorentz-structures, Dark energy and Exotic smoothness On 4-dimensional Lorentz-structures, Dark energy and Exotic smoothness

2011-10-31

arxiv.org/abs/1110.6768v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

7 pages, no figures, PACS 04.20.Gz, 98.80.Jk, 95.36.+x an obvious error in the notation of the hyperbolic 3-manifold was fixed

Scientific paper

Usually, the topology of a 4-manifolds $M$ is restricted to admit a global hyperbolic structure $\Sigma\times\mathbb{R}$. The result was obtained by using two conditions: existence of a Lorentz structure and causality (no time-like closed curves). In this paper we study the influence of the smoothness structure to show its independence of the two conditions. Then we obtain the possibility for a topology-change of the 3-manifold $\Sigma$ keeping fix its homology. We will study the example $S^{3}\times\mathbb{R}$ with an exotic differential structure more carefully to show some implications for cosmology. Especially we obtain an interpretation of the transition in topology as dark energy.

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