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Construction of Oscillatory Singularities

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Progress in Mathematical Relativity, Gravitation and Cosmology

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 60))

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Abstract

One way to understand more about spacetime singularities is to construct solutions of the Einstein equations containing singularities with prescribed properties. The heuristic ideas of the BKL picture suggest that oscillatory singularities should be very common and give a detailed picture of how these could look. The more straightforward case of singularities without oscillations is reviewed and existing results on that subject are surveyed. Then recent theorems proving the existence of spatially homogeneous solutions with oscillatory singularities of a specific type are presented. The proofs of these involve applications of some ideas concerning heteroclinic chains and their stability. Some necessary background from the theory of dynamical systems is explained. Finally some directions in which this research might be generalized in the future are pointed out.

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Author information

Authors and Affiliations

  1. Max Planck Institute for Gravitational Physics, Am Mühlenberg 1, 14476, Potsdam, Germany

    Alan D. Rendall

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  1. Alan D. Rendall
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Correspondence to Alan D. Rendall .

Editor information

Editors and Affiliations

  1. Dept. of Mathematics, University of Minho, Braga, Portugal

    Alfonso García-Parrado

  2. Dept. of Mathematics, University of Minho, Braga, Portugal

    Filipe C. Mena

  3. Dept. of Mathematics, University of Minho, Braga, Portugal

    Filipe Moura

  4. Dept. of Mathematics, University of Minho, Braga, Portugal

    Estelita Vaz

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Rendall, A.D. (2014). Construction of Oscillatory Singularities. In: García-Parrado, A., Mena, F., Moura, F., Vaz, E. (eds) Progress in Mathematical Relativity, Gravitation and Cosmology. Springer Proceedings in Mathematics & Statistics, vol 60. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40157-2_7

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