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arXiv · 1201.3716

Sur la géométrie de la singularité initiale des espaces-temps plats globalement hyperboliques

Mehdi Belraouti
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Abstract

Let $M$ be a maximal globally hyperbolic Cauchy compact flat spacetime of dimension 2+1, admitting a Cauchy hypersurface diffeomorphic to a compact hyperbolic manifold. We study the asymptotic behaviour of level sets of quasi-concave time functions on $M$. We give a positive answer to a conjecture of Benedetti and Guadagnini in \cite{MR1857817}. More precisely, we prove that the level sets of such a time function converge in the Hausdorff-Gromov equivariant topology to a real tree. Moreover, this limit does not depend on the choice of the time function.

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Mehdi Belraouti. 2012-01-18. Sur la géométrie de la singularité initiale des espaces-temps plats globalement hyperboliques. https://arxiv.org/abs/1201.3716

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