5 research outputs found
Evidence for an oscillatory singularity in generic U(1) symmetric cosmologies on
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 . 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.Comment: 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/u1genfig
Numerical Evidence that the Singularity in Polarized U(1) Symmetric Cosmologies on is Velocity Dominated
Numerical evidence supports the conjecture that polarized U(1) symmetric
cosmologies have asymptotically velocity term dominated singularities.Comment: 8 pages, RevTex, 4 figures, uses eps
Phenomenology of the Gowdy Universe on
Numerical studies of the plane symmetric, vacuum Gowdy universe on yield strong support for the conjectured asymptotically velocity term
dominated (AVTD) behavior of its evolution toward the singularity except,
perhaps, at isolated spatial points. A generic solution is characterized by
spiky features and apparent ``discontinuities'' in the wave amplitudes. It is
shown that the nonlinear terms in the wave equations drive the system
generically to the ``small velocity'' AVTD regime and that the spiky features
are caused by the absence of these terms at isolated spatial points.Comment: 19 pages, 21 figures, uses Revtex, psfi