Spacetime Singularities: Recent Developments

Abstract

Recent developments concerning oscillatory spacelike singularities in general relativity are taking place on two fronts. The first treats generic singularities in spatially homogeneous cosmology, most notably Bianchi types VIII and IX. The second deals with generic oscillatory singularities in inhomogeneous cosmologies, especially those with two commuting spacelike Killing vectors. This paper describes recent progress in these two areas: in the spatially homogeneous case focus is on mathematically rigorous results, while analytical and numerical results concerning generic behavior and so-called recurring spike formation are the main topic in the inhomogeneous case. Unifying themes are connections between asymptotic behavior, hierarchical structures, and solution generating techniques, which provide hints for a link between the nature of generic singularities and a hierarchy of hidden asymptotic symmetries.

21 pages, 7 figures (16 PDF figure files), plenary contribution to the Proceedings of the Thirteenth Marcel Grossmann Meeting

References in corpus (5)

• Spikes in the Mixmaster regime of G_2 cosmologies
• Mixmaster: Fact and Belief
• New explicit spike solution -- non-local component of the generalized Mixmaster attractor
• A new proof of the Bianchi type IX attractor theorem
• Statistical Properties of Cosmological Billiards

Cited by in corpus (10)

• Recent developments concerning generic spacelike singularities
• On the dynamics of the general Bianchi IX spacetime near the singularity
• Mathematical General Relativity
• Open problems in mathematical physics
• Cosmological global dynamical systems analysis
• On The Dynamics of a Closed Viscous Universe
• Curvature invariants for the Bianchi IX spacetime filled with tilted dust
• Spike statistics
• Chaos in spatially homogeneous Hořava-Lifshitz subcritical cosmologies
• Periodic orbits in Hořava-Lifshitz cosmologies