Approach to the Singularity in Spatially Inhomogeneous Cosmologies

Details Approach to the Singularity in Spatially Inhomogeneous Cosmologies Approach to the Singularity in Spatially Inhomogeneous Cosmologies

2001-06-04

arxiv.org/abs/gr-qc/0106009v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

17 pages, in Differential Equations and Mathematical Physics : Proceedings of an International Conference Held at the Universi

Scientific paper

A combination of analytic and numerical methods has yielded a clear understanding of the approach to the singularity in spatially inhomogeneous cosmologies. Strong support is found for the longstanding claim by Belinskii, Khalatnikov, and Lifshitz that the collapse is dominated by local Kasner or Mixmaster behavior. The Method of Consistent Potentials is used to establish the consistency of asymptotic velocity term dominance (AVTD) (local Kasner behavior) in that no terms in Einstein's equations will grow exponentially when the VTD solution, obtained by neglecting all terms containing spatial derivatives, is substituted into the full equations. When the VTD solution is inconsistent, the exponential terms act dynamically as potentials either to drive the system into a consistent AVTD regime or to maintain an oscillatory approach to the singularity.

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