Evidence for an oscillatory singularity in generic U(1) symmetric cosmologies on $T^3\times R$

Abstract

A longstanding conjecture by Belinskii, Lifshitz, and Khalatnikov that the singularity in generic gravitational collapse is locally oscillatory is tested numerically in vacuum, U(1) symmetric cosmological spacetimes on $T^3\times R$. If the velocity term dominated (VTD) solution to Einstein's equations is substituted into the Hamiltonian for the full Einstein evolution equations, one term is found to grow exponentially. This generates a prediction that oscillatory behavior involving this term and another (which the VTD solution causes to decay exponentially) should be observed in the approach to the singularity. Numerical simulations strongly support this prediction.

15 pages, Revtex, includes 12 figures, psfig. High resolution versions of figures 7, 8, 9, and 11 may be obtained from anonymous ftp to ftp://vela.acs.oakland.edu/pub/berger/u1genfigs

References in corpus (5)

• Analytic description of singularities in Gowdy spacetimes
• Mixmaster Behavior in Inhomogeneous Cosmological Spacetimes
• Global Foliations of Vacuum Spacetimes with $T^2$ Isometry
• Phenomenology of the Gowdy Universe on $T^3\times R$
• Numerical Evidence that the Singularity in Polarized U(1) Symmetric Cosmologies on $T^3\times R$ is Velocity Dominated

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