The cosmological billiard attractor. (English) Zbl 1170.83003

This paper represents a nice overview about a large class of exact and approximate solutions of Einstein’s field equation. Their common point of view is a similarity with a mechanical problem: the motion of a point mass in a space with boundary. This explains the title of this paper: the solutions often behave like a billiard ball having a couple of reflections at the boundary before vanishing in the hole. Typically, the examples are of spatially homogeneous geometry, and already the vacuum case gives interesting details. In other papers, the notion “mixmaster model” is used for this kind of solutions.


83-02 Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory
83C75 Space-time singularities, cosmic censorship, etc.
83C15 Exact solutions to problems in general relativity and gravitational theory
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
83F05 Relativistic cosmology


mixmaster model
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