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arXiv · 1110.6768

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

T. Asselmeyer-Maluga·R. Mader·J. Krol
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Abstract

Usually, the topology of a 4-manifolds $M$ is restricted to admit a global hyperbolic structure $Σ\times\mathbb{R}$. 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 $Σ$ 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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BibTeXRIS

T. Asselmeyer-Maluga, R. Mader, J. Krol. 2011-11-03. On 4-dimensional Lorentz-structures, Dark energy and Exotic smoothness. https://arxiv.org/abs/1110.6768

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