332 research outputs found
Scale-factor duality in string Bianchi cosmologies
We apply the scale factor duality transformations introduced in the context
of the effective string theory to the anisotropic Bianchi-type models. We find
dual models for all the Bianchi-types [except for types and ] and
construct for each of them its explicit form starting from the exact original
solution of the field equations. It is emphasized that the dual Bianchi class
models require the loss of the initial homogeneity symmetry of the
dilatonic scalar field.Comment: 18 pages, no figure
Optimum quantisers for a Gaussian input probability density and for the magnitude-error distortion measure
The parameters of non-uniform and uniform quantizers up to ten bits of quantization, optimum for a Gaussian input probability and for the magnitude-error distortion criterion are computed. Optimum quantizers must be understood as quantizers with minimum distortion. The numerical method used for the optimization converges relatively rapidly. The comparison between optimum non-uniform quantizers and optimum uniform quantizers is made
The Behavior of Kasner Cosmologies with Induced Matter
We extend the induced matter model, previously applied to a variety of
isotropic cases, to a generalization of Bianchi type-I anisotropic cosmologies.
The induced matter model is a 5D Kaluza-Klein approach in which assumptions of
compactness are relaxed for the fifth coordinate, leading to extra geometric
terms. One interpretation of these extra terms is to identify them as an
``induced matter'' contribution to the stress-energy tensor. In similar spirit,
we construct a five dimensional metric in which the spatial slices possess
Bianchi type-I geometry. We find a set of solutions for the five dimensional
Einstein equations, and determine the pressure and density of induced matter.
We comment on the long-term dynamics of the model, showing that the assumption
of positive density leads to the contraction over time of the fifth scale
factor.Comment: 14 page
Some remarks on singularities in quantum cosmology
We discuss to what extent classical singularities persist upon quantization
in two simple cosmological models.Comment: 4 pps., LaTeX2e. Substantial revisions. To appear in: Proc. of the
Second Conference on Constrained Dynamics and Quantum Gravity, Santa
Margherita Ligure, Italy, 17-21 September 1996. Edited by V. de Alfaro et a
Solutions of Higher Dimensional Gauss-Bonnet FRW Cosmology
We examine the effect on cosmological evolution of adding a Gauss-Bonnet term
to the standard Einstein-Hilbert action for a (1 + 3)+ d dimensional
Friedman-Robertson-Walker (FRW) metric. By assuming that the additional
dimensions compactify as a power law as the usual 3 spatial dimensions expand,
we solve the resulting dynamical equations and find that the solution may be of
either de Sitter or Kasner form depending upon whether the Gauss-Bonnet term or
the Einstein term dominates.Comment: 10 pages, references added/corrected, accepted for publication in
General Relativity and Gravitatio
Supergravity Black Holes and Billiards and Liouville integrable structure of dual Borel algebras
In this paper we show that the supergravity equations describing both cosmic
billiards and a large class of black-holes are, generically, both Liouville
integrable as a consequence of the same universal mechanism. This latter is
provided by the Liouville integrable Poissonian structure existing on the dual
Borel algebra B_N of the simple Lie algebra A_{N-1}. As a by product we derive
the explicit integration algorithm associated with all symmetric spaces U/H^{*}
relevant to the description of time-like and space-like p-branes. The most
important consequence of our approach is the explicit construction of a
complete set of conserved involutive hamiltonians h_{\alpha} that are
responsible for integrability and provide a new tool to classify flows and
orbits. We believe that these will prove a very important new tool in the
analysis of supergravity black holes and billiards.Comment: 48 pages, 7 figures, LaTex; V1: misprints corrected, two references
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Billiard Representation for Multidimensional Quantum Cosmology near the Singularity
The degenerate Lagrangian system describing a lot of cosmological models is
considered. When certain restrictions on the parameters of the model are
imposed, the dynamics of the model near the "singularity" is reduced to a
billiard on the Lobachevsky space. The Wheeler-DeWitt equation in the
asymptotical regime is solved and a third-quantized model is suggested.Comment: 6 pages, LaTe
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