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

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

1998-04-30

arxiv.org/abs/gr-qc/9804085v1

Phys.Rev. D58 (1998) 064023

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, Revtex, includes 12 figures, psfig. High resolution versions of figures 7, 8, 9, and 11 may be obtained from anonymo

Scientific paper

10.1103/PhysRevD.58.064023

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.

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