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Beverly K. Berger

Publications and source records attributed to Beverly K. Berger.

27 records · Page 2Linked to original sources
arXiv1998

On the Nature of the Generic Big Bang

Spatially homogeneous but possibly anisotropic cosmologies have two main types of singularities: (1) asymptotically velocity term dominated (AVTD) - (reversing the time direction) the universe evolves to the singularity with fixed anisotropic collapse rates ; (2) Mixmaster-the anisotropic collapse rates change in a deterministicaly chaotic way. Much less is known about spatially inhomogeneous universes. It has been claimed that a generic universe would evolve toward the singularity as a different Mixmaster universe at each spatial point. I shall discuss how to predict whether a cosmology has an AVTD or Mixmaster singularity and whether or not our numerical simulations agree with these predictions.

gr-qc↗
arXiv1997

Phenomenology of the Gowdy Universe on $T^3 \times R$

Numerical studies of the plane symmetric, vacuum Gowdy universe on $T^3 \times R$ 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.

gr-qc↗
arXiv1997

Comment on ``The Gowdy $T^3$ Cosmologies Revisited''

A standard and reasonable definition of asymptotic velocity term dominance (AVTD) shows that the numerical study by Hern and Stewart (gr-qc/9708038) confirms previous results that generic Gowdy cosmologies on $T^3 \times R$ have an AVTD singularity.

gr-qc↗
arXiv1997

Global Foliations of Vacuum Spacetimes with $T^2$ Isometry

We prove a global existence theorem (with respect to a geometrically- defined time) for globally hyperbolic solutions of the vacuum Einstein equations which admit a $T^2$ isometry group with two-dimensional spacelike orbits, acting on $T^3$ spacelike surfaces.

gr-qc↗
arXiv1996

New Algorithm for Mixmaster Dynamics

We present a new numerical algorithm for evolving the Mixmaster spacetimes. By using symplectic integration techniques to take advantage of the exact Taub solution for the scattering between asymptotic Kasner regimes, we evolve these spacetimes with higher accuracy using much larger time steps than previously possible. The longer Mixmaster evolution thus allowed enables detailed comparison with the Belinskii, Khalatnikov, Lifshitz (BKL) approximate Mixmaster dynamics. In particular, we show that errors between the BKL prediction and the measured parameters early in the simulation can be eliminated by relaxing the BKL assumptions to yield an improved map. The improved map has different predictions for vacuum Bianchi Type IX and magnetic Bianchi Type VI$_0$ Mixmaster models which are clearly matched in the simulation.

gr-qc↗
arXiv1995

Numerical Investigation of Singularities

Numerical exploration of the properties of singularities could, in principle, yield detailed understanding of their nature in physically realistic cases. Examples of numerical investigations into the formation of naked singularities, critical behavior in collapse, passage through the Cauchy horizon, chaos of the Mixmaster singularity, and singularities in spatially inhomogeneous cosmololgies are discussed.

gr-qc↗
arXiv1995

Numerical Investigation of Cosmological Singularities

We describe a numerical approach to address the BKL conjecture that the generic cosmological singularity is locally Mixmaster-like. We consider application of a symplectic PDE solver to three models of increasing complexity--spatially homogeneous (vacuum) Mixmaster cosmologies where we compare the symplectic ODE solver to a Runge-Kutta one, the (plane symmetric, vacuum) Gowdy universe on $T^3 \times R$ whose dynamical degrees of freedom satisfy nonlinearly coupled PDE's in one spatial dimension and time, and U(1) symmetric, vacuum cosmologies on $T^3 \times R$ which are the simplest spatially inhomogeneous universes in which local Mixmaster dynamics is allowed.

gr-qc↗