On the Nature of the Generic Cosmological Singularity

Details On the Nature of the Generic Cosmological Singularity On the Nature of the Generic Cosmological Singularity

Apr 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998aps..apr.i2204b&link_type=abstract

American Physical Society, APS/AAPT Joint April Meeting, April 18-21, 1998 Columbus, Ohio, abstract #I22.04

Mathematics

Logic

Scientific paper

The nature of the singularity in generic gravitational collapse remains an important open question in general relativity. To study this problem requires a synthesis of analytic and numerical techniques. One evolves numerically toward the singularity sufficiently far to identify the asymptotic behavior which characterizes it. To simplify the boundary conditions, spatially inhomogeneous cosmological spacetimes on T^3 × R are studied. It is found that the asymptotic approach to the singularity is local (each spatial point evolves toward the singularity as a different spatially homogeneous universe) as was claimed long ago by Belinskii, Khalatnikov, and Lifshitz (BKL). In vacuum Gowdy (plane-symmetric) models and polarized U(1) symmetric models, the local asymptotic behavior is Kasner-like (asymptotically velocity term dominated) while in magnetic generalized Gowdy and (possibly) in generic U(1) models it is Mixmaster-like---as conjectured by BKL for the general solution to Einstein's equations. The use of symplectic PDE solvers in the numerical simulations leads naturally to consideration of the effect of the nonlinear terms in the Hamiltonians. Exponential factors in such terms act locally to control the asymptotic approach to the singularity. This feature can be exploited analytically to predict the nature of the asymptotic behavior. So far, these predictions have been supported by the numerical simulations and reinforce the evidence for the local nature of the final stages of generic gravitational collapse.

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