Kasner-like behaviour for subcritical Einstein-matter systems

Abstract

Confirming previous heuristic analyses à la Belinskii-Khalatnikov-Lifshitz, it is rigorously proven that certain ``subcritical'' Einstein-matter systems exhibit a monotone, generalized Kasner behaviour in the vicinity of a spacelike singularity. The D-dimensional coupled Einstein-dilaton-p-form system is subcritical if the dilaton couplings of the p-forms belong to some dimension dependent open neighbourhood of zero, while pure gravity is subcritical if D is greater than or equal to 11. Our proof relies, like the recent theorem dealing with the (always subcritical) Einstein-dilaton system, on the use of Fuchsian techniques, which enable one to construct local, analytic solutions to the full set of equations of motion. The solutions constructed are ``general'' in the sense that they depend on the maximal expected number of free functions.

LaTeX, 56 pages; minor corrections; version to appear in ``Annales Henri Poincaré"

References in corpus (20)

• The String Dilaton and a Least Coupling Principle
• Quintessence as a run-away dilaton
• Quiescent cosmological singularities
• Chaos in Superstring Cosmology
• Harmonic coordinate method for simulating generic singularities
• E_(10), BE_(10) and Arithmetical Chaos in Superstring Cosmology
• String Theory and Inflation
• Fuchsian analysis of singularities in Gowdy spacetimes beyond analyticity
• Einstein Constraints on Asymptotically Euclidean Manifolds
• Mixmaster Behavior in Inhomogeneous Cosmological Spacetimes
• Evidence for an oscillatory singularity in generic U(1) symmetric cosmologies on $T^3\times R$
• Phenomenology of the Gowdy Universe on $T^3\times R$
• Oscillatory approach to the singularity in vacuum spacetimes with $T^2$ isometry
• Dynamics of magnetic Bianchi VI_0 cosmologies
• Influence of scalar fields on the approach to a cosmological singularity
• Dynamics of inhomogeneities of metric in the vicinity of a singularity in multidimensional cosmology authors
• Exact U(1) symmetric cosmologies with local Mixmaster dynamics
• Asymptotic singular behavior of Gowdy spacetimes in string theory
• Applications of the theory of evolution equations to general relativity
• A class of perfect-fluid cosmologies with polarised Gowdy symmetry and a Kasner-like singularity

Cited by in corpus (1)

• Gravitational Billiards, Dualities and Hidden Symmetries