62 research outputs found
Hyperextended Scalar-Tensor Gravity
We study a general Scalar-Tensor Theory with an arbitrary coupling funtion
but also an arbitrary dependence of the ``gravitational
constant'' in the cases in which either one of them, or both, do not
admit an analytical inverse, as in the hyperextended inflationary scenario. We
present the full set of field equations and study their cosmological behavior.
We show that different scalar-tensor theories can be grouped in classes with
the same solution for the scalar field.Comment: latex file, To appear in Physical Review
Some exact non-vacuum Bianchi VI0 and VII0 instantons
We report some new exact instantons in general relativity. These solutions
are K\"ahler and fall into the symmetry classes of Bianchi types VI0 and VII0,
with matter content of a stiff fluid. The qualitative behaviour of the
solutions is presented, and we compare it to the known results of the
corresponding self-dual Bianchi solutions. We also give axisymmetric Bianchi
VII0 solutions with an electromagnetic field.Comment: latex, 15 pages with 3 eps figure
Non-Vacuum Bianchi Types I and V in f(R) Gravity
In a recent paper \cite{1}, we have studied the vacuum solutions of Bianchi
types I and V spacetimes in the framework of metric f(R) gravity. Here we
extend this work to perfect fluid solutions. For this purpose, we take stiff
matter to find energy density and pressure of the universe. In particular, we
find two exact solutions in each case which correspond to two models of the
universe. The first solution gives a singular model while the second solution
provides a non-singular model. The physical behavior of these models has been
discussed using some physical quantities. Also, the function of the Ricci
scalar is evaluated.Comment: 15 pages, accepted for publication in Gen. Realtiv. Gravi
Isotropization of Bianchi-Type Cosmological Solutions in Brans-Dicke Theory
The cosmic, general analitic solutions of the Brans--Dicke Theory for the
flat space of homogeneous and isotropic models containing perfect, barotropic,
fluids are seen to belong to a wider class of solutions --which includes
cosmological models with the open and the closed spaces of the
Friedmann--Robertson--Walker metric, as well as solutions for models with
homogeneous but anisotropic spaces corresponding to the Bianchi--Type metric
clasification-- when all these solutions are expressed in terms of reduced
variables. The existence of such a class lies in the fact that the scalar
field, , times a function of the mean scale factor or ``volume element'',
, which depends on time and on the barotropic index of the
equation of state used, can be written as a function of a ``cosmic time''
reduced in terms of another function of the mean scale factor depending itself
again on the barotropic index but independent of the metrics here employed.
This reduction procedure permites one to analyze if explicitly given
anisotropic cosmological solutions ``isotropize'' in the course of their time
evolution. For if so can happen, it could be claimed that there exists a
subclass of solutions that is stable under anisotropic perturbations.Comment: 15 pages, Late
The conformal status of Brans-Dicke cosmology
Following recent fit of supernovae data to Brans-Dicke theory which favours
the model with \cite{fabris} we discuss the status of this
special case of Brans-Dicke cosmology in both isotropic and anisotropic
framework. It emerges that the limit is consistent only with
the vacuum field equations and it makes such a Brans-Dicke theory conformally
invariant. Then it is an example of the conformal relativity theory which
allows the invariance with respect to conformal transformations of the metric.
Besides, Brans-Dicke theory with gives a border between a
standard scalar field model and a ghost/phantom model.
In this paper we show that in Brans-Dicke theory, i.e., in
the conformal relativity there are no isotropic Friedmann solutions of non-zero
spatial curvature except for case. Further we show that this
case, after the conformal transformation into the Einstein frame, is just the
Milne universe and, as such, it is equivalent to Minkowski spacetime. It
generally means that only flat models are fully consistent with the field
equations. On the other hand, it is shown explicitly that the anisotropic
non-zero spatial curvature models of Kantowski-Sachs type are admissible in
Brans-Dicke theory. It then seems that an additional scale
factor which appears in anisotropic models gives an extra deegre of freedom and
makes it less restrictive than in an isotropic Friedmann case.Comment: REVTEX4, 19 pages, 8 figures, references adde
Multidimensional Cosmology: Spatially Homogeneous models of dimension 4+1
In this paper we classify all 4+1 cosmological models where the spatial
hypersurfaces are connected and simply connected homogeneous Riemannian
manifolds. These models come in two categories, multiply transitive and simply
transitive models. There are in all five different multiply transitive models
which cannot be considered as a special case of a simply transitive model. The
classification of simply transitive models, relies heavily upon the
classification of the four dimensional (real) Lie algebras. For the orthogonal
case, we derive all the equations of motion and give some examples of exact
solutions. Also the problem of how these models can be compactified in context
with the Kaluza-Klein mechanism, is addressed.Comment: 24 pages, no figures; Refs added, typos corrected. To appear in CQ
Integration of D-dimensional 2-factor spaces cosmological models by reducing to the generalized Emden-Fowler equation
The D-dimensional cosmological model on the manifold describing the evolution of 2 Einsteinian factor spaces,
and , in the presence of multicomponent perfect fluid source is
considered. The barotropic equation of state for mass-energy densities and the
pressures of the components is assumed in each space. When the number of the
non Ricci-flat factor spaces and the number of the perfect fluid components are
both equal to 2, the Einstein equations for the model are reduced to the
generalized Emden-Fowler (second-order ordinary differential) equation, which
has been recently investigated by Zaitsev and Polyanin within discrete-group
analysis. Using the integrable classes of this equation one generates the
integrable cosmological models. The corresponding metrics are presented. The
method is demonstrated for the special model with Ricci-flat spaces
and the 2-component perfect fluid source.Comment: LaTeX file, no figure
Toda chains with type A_m Lie algebra for multidimensional m-component perfect fluid cosmology
We consider a D-dimensional cosmological model describing an evolution of
Ricci-flat factor spaces, M_1,...M_n (n > 2), in the presence of an m-component
perfect fluid source (n > m > 1). We find characteristic vectors, related to
the matter constants in the barotropic equations of state for fluid components
of all factor spaces.
We show that, in the case where we can interpret these vectors as the root
vectors of a Lie algebra of Cartan type A_m=sl(m+1,C), the model reduces to the
classical open m-body Toda chain.
Using an elegant technique by Anderson (J. Math. Phys. 37 (1996) 1349) for
solving this system, we integrate the Einstein equations for the model and
present the metric in a Kasner-like form.Comment: LaTeX, 2 ps figure
Bianchi type II,III and V diagonal Einstein metrics re-visited
We present, for both minkowskian and euclidean signatures, short derivations
of the diagonal Einstein metrics for Bianchi type II, III and V. For the first
two cases we show the integrability of the geodesic flow while for the third
case a somewhat unusual bifurcation phenomenon takes place: for minkowskian
signature elliptic functions are essential in the metric while for euclidean
signature only elementary functions appear
Further results on non-diagonal Bianchi type III vacuum metrics
We present the derivation, for these vacuum metrics, of the Painlev\'e VI
equation first obtained by Christodoulakis and Terzis, from the field equations
for both minkowskian and euclidean signatures. This allows a complete
discussion and the precise connection with some old results due to Kinnersley.
The hyperk\"ahler metrics are shown to belong to the Multi-Centre class and for
the cases exhibiting an integrable geodesic flow the relevant Killing tensors
are given. We conclude by the proof that for the Bianchi B family, excluding
type III, there are no hyperk\"ahler metrics.Comment: 21 pages, no figure
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