90 research outputs found
Comment on the chaotic singularity in some magnetic Bianchi VI cosmologies
Description of the magnetic Bianchi VI cosmologies of LeBlanc, Kerr, and
Wainwright in the formalisms both of Belinskii, Khalatnikov, and Lifshitz, and
of Misner allows qualitative understanding of the Mixmaster-like singularity in
those models.Comment: 8 pages, Revtex, no figure
Report on A5. Computer Methods
Session A5 on numerical methods contained talks on colliding black holes,
critical phenomena, investigation of singularities, and computer algebra.Comment: 9 pages, for GR16 proceeding
Influence of scalar fields on the approach to a cosmological singularity
The method of consistent potentials is used to explain how a minimally
coupled (classical) scalar field can suppress Mixmaster oscillations in the
approach to the singularity of generic cosmological spacetimes.Comment: 8 pages includes 5 figures. Uses revtex, psfi
Approach to the Singularity in Spatially Inhomogeneous Cosmologies
A combination of analytic and numerical methods has yielded a clear
understanding of the approach to the singularity in spatially inhomogeneous
cosmologies. Strong support is found for the longstanding claim by Belinskii,
Khalatnikov, and Lifshitz that the collapse is dominated by local Kasner or
Mixmaster behavior. The Method of Consistent Potentials is used to establish
the consistency of asymptotic velocity term dominance (AVTD) (local Kasner
behavior) in that no terms in Einstein's equations will grow exponentially when
the VTD solution, obtained by neglecting all terms containing spatial
derivatives, is substituted into the full equations. When the VTD solution is
inconsistent, the exponential terms act dynamically as potentials either to
drive the system into a consistent AVTD regime or to maintain an oscillatory
approach to the singularity.Comment: 17 pages, in Differential Equations and Mathematical Physics :
Proceedings of an International Conference Held at the University of Alabama
in Birmingham, ed. by R. Weikard, G. Weinstein (American Mathematical
Society, 2000
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 whose dynamical degrees of freedom
satisfy nonlinearly coupled PDE's in one spatial dimension and time, and U(1)
symmetric, vacuum cosmologies on which are the simplest
spatially inhomogeneous universes in which local Mixmaster dynamics is allowed.Comment: Based on lectures given at WE-Heraeus-Seminar on Relativity and
Scientific Computing. 24 pages, Latex, 9 figures in separate file BHfigs.uu,
uses psfig.te
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.Comment: Based on GR14 talk. 21 pages, Latex, 5 figures in separate file
gr14.uu. Uses sprocl.sty, psfig.st
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.Comment: 7 pages, 5 figures, uses Revtex, epsf. Based on talk given at
Symposium on Frontiers of Fundamental Physics, Hyderabad, India, 11-12 Dec
199
Signature for local Mixmaster dynamics in U(1) symmetric cosmologies
Previous studies \cite{berger98a} have provided strong support for a local,
oscillatory approach to the singularity in U(1) symmetric, spatially
inhomogeneous vacuum cosmologies on . The description of a vacuum
Bianchi type IX, spatially homogeneous Mixmaster cosmology (on )
in terms of the variables used to describe the U(1) symmetric cosmologies
indicates that the oscillations in the latter are in fact those of local
Mixmaster dynamics. One of the variables of the U(1) symmetric models increases
only at the end of a Mixmaster era. Such an increase therefore yields a
qualitative signature for local Mixmaster dynamics in spatially inhomogeneous
cosmologies.Comment: 13 pages, uses RevTex, psfi
Exact U(1) symmetric cosmologies with local Mixmaster dynamics
By applying a standard solution generating technique, we transform an
arbitrary vacuum Mixmaster solution on to a new solution
which is spatially inhomogeneous. We thereby obtain a family of exact,
spatially inhomogeneous, vacuum spacetimes which exhibit Belinskii,
Khalatnikov, and Lifshitz (BKL) oscillatory behavior. The solutions are
constructed explicitly by performing the transformations on numerically
generated, homogeneous Mixmaster solutions. Their behavior is found to be
qualitatively like that seen in previous numerical simulations of generic U(1)
symmetric cosmological spacetimes on .Comment: 13 pages, 5 figures, uses RevTeX and psfi
Stability Within -Symmetric Expanding Spacetimes
We prove a nonpolarised analogue of the asymptotic characterization of
-symmetric Einstein Flow solutions completed recently by LeFloch and
Smulevici. In this work, we impose a condition weaker than polarisation and so
our result applies to a larger class. We obtain similar rates of decay for the
normalized energy and associated quantities for this class. We describe
numerical simulations which indicate that there is a locally attractive set for
-symmetric solutions not covered by our main theorem. This local attractor
is distinct from the local attractor in our main theorem, thereby indicating
that the polarised asymptotics are unstable.Comment: 19 pages, 5 figure
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