Construction of oscillatory singularities

Rendall, Alan D.

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Construction of oscillatory singularities

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Rendall, Alan D.
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1212.5418
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Rendall, A. D. (2014). Construction of oscillatory singularities. In A. García-Parrado (Ed.), Proceedings of the Spanish Relativity Meeting (ERES 2012) Progress in Mathematical Relativity, Gravitation and Cosmology, Springer Proceedings in Mathematics & Statistics 60 (pp. 95-105). Berlin Heidelberg: Springer.

Cite as: https://hdl.handle.net/11858/00-001M-0000-000E-74CA-3

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.