341 research outputs found
A Non - Singular Cosmological Model with Shear and Rotation
We have investigated a non-static and rotating model of the universe with an
imperfect fluid distribution. It is found that the model is free from
singularity and represents an ever expanding universe with shear and rotation
vanishing for large value of time.Comment: 10 pages, late
Essential Constants for Spatially Homogeneous Ricci-flat manifolds of dimension 4+1
The present work considers (4+1)-dimensional spatially homogeneous vacuum
cosmological models. Exact solutions -- some already existing in the
literature, and others believed to be new -- are exhibited. Some of them are
the most general for the corresponding Lie group with which each homogeneous
slice is endowed, and some others are quite general. The characterization
``general'' is given based on the counting of the essential constants, the
line-element of each model must contain; indeed, this is the basic contribution
of the work. We give two different ways of calculating the number of essential
constants for the simply transitive spatially homogeneous (4+1)-dimensional
models. The first uses the initial value theorem; the second uses, through
Peano's theorem, the so-called time-dependent automorphism inducing
diffeomorphismsComment: 26 Pages, 2 Tables, latex2
Towards Canonical Quantum Gravity for G1 Geometries in 2+1 Dimensions with a Lambda--Term
The canonical analysis and subsequent quantization of the (2+1)-dimensional
action of pure gravity plus a cosmological constant term is considered, under
the assumption of the existence of one spacelike Killing vector field. The
proper imposition of the quantum analogues of the two linear (momentum)
constraints reduces an initial collection of state vectors, consisting of all
smooth functionals of the components (and/or their derivatives) of the spatial
metric, to particular scalar smooth functionals. The demand that the
midi-superspace metric (inferred from the kinetic part of the quadratic
(Hamiltonian) constraint) must define on the space of these states an induced
metric whose components are given in terms of the same states, which is made
possible through an appropriate re-normalization assumption, severely reduces
the possible state vectors to three unique (up to general coordinate
transformations) smooth scalar functionals. The quantum analogue of the
Hamiltonian constraint produces a Wheeler-DeWitt equation based on this reduced
manifold of states, which is completely integrated.Comment: Latex 2e source file, 25 pages, no figures, final version (accepted
in CQG
Bianchi type-II cosmological model: some remarks
Within the framework of Bianchi type-II (BII) cosmological model the behavior
of matter distribution has been considered. It is shown that the non-zero
off-diagonal component of Einstein tensor implies some severe restriction on
the choice of matter distribution. In particular for a locally rotationally
symmetric Bianchi type-II (LRS BII) space-time it is proved that the matter
distribution should be strictly isotropic if the corresponding matter field
possesses only non-zero diagonal components of the energy-momentum tensor.Comment: 3 page
Future geodesic completeness of some spatially homogeneous solutions of the vacuum Einstein equations in higher dimensions
It is known that all spatially homogeneous solutions of the vacuum Einstein
equations in four dimensions which exist for an infinite proper time towards
the future are future geodesically complete. This paper investigates whether
the analogous statement holds in higher dimensions. A positive answer to this
question is obtained for a large class of models which can be studied with the
help of Kaluza-Klein reduction to solutions of the Einstein-scalar field
equations in four dimensions. The proof of this result makes use of a criterion
for geodesic completeness which is applicable to more general spatially
homogeneous models.Comment: 18 page
Words with the Maximum Number of Abelian Squares
An abelian square is the concatenation of two words that are anagrams of one
another. A word of length can contain distinct factors that
are abelian squares. We study infinite words such that the number of abelian
square factors of length grows quadratically with .Comment: To appear in the proceedings of WORDS 201
Indeterminate strings, prefix arrays & undirected graphs
An integer array y=y[1..n] is said to be feasible if and only if y[1]=n and, for every i∈2..n, i≤i+y[i]≤n+1. A string is said to be indeterminate if and only if at least one of its elements is a subset of cardinality greater than one of a given alphabet Σ; otherwise it is said to be regular. A feasible array y is said to be regular if and only if it is the prefix array of some regular string. We show using a graph model that every feasible array of integers is a prefix array of some (indeterminate or regular) string, and for regular strings corresponding to y, we use the model to provide a lower bound on the alphabet size. We show further that there is a 1–1 correspondence between labelled simple graphs and indeterminate strings, and we show how to determine the minimum alphabet size σ of an indeterminate string x based on its associated graph Gx. Thus, in this sense, indeterminate strings are a more natural object of combinatorial interest than the strings on elements of Σ that have traditionally been studied
Vacuum Plane Waves in 4+1 D and Exact solutions to Einstein's Equations in 3+1 D
In this paper we derive homogeneous vacuum plane-wave solutions to Einstein's
field equations in 4+1 dimensions. The solutions come in five different types
of which three generalise the vacuum plane-wave solutions in 3+1 dimensions to
the 4+1 dimensional case. By doing a Kaluza-Klein reduction we obtain solutions
to the Einstein-Maxwell equations in 3+1 dimensions. The solutions generalise
the vacuum plane-wave spacetimes of Bianchi class B to the non-vacuum case and
describe spatially homogeneous spacetimes containing an extremely tilted fluid.
Also, using a similar reduction we obtain 3+1 dimensional solutions to the
Einstein equations with a scalar field.Comment: 16 pages, no figure
Automorphisms of Real 4 Dimensional Lie Algebras and the Invariant Characterization of Homogeneous 4-Spaces
The automorphisms of all 4-dimensional, real Lie Algebras are presented in a
comprehensive way. Their action on the space of , real, symmetric
and positive definite, matrices, defines equivalence classes which are used for
the invariant characterization of the 4-dimensional homogeneous spaces which
possess an invariant basis.Comment: LaTeX2e, 23 pages, 2 Tables. To appear in Journal of Physics A:
Mathematical & Genera
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