374 research outputs found
Uniqueness of Petrov type D spatially inhomogeneous irrotational silent models
The consistency of the constraint with the evolution equations for spatially
inhomogeneous and irrotational silent (SIIS) models of Petrov type I, demands
that the former are preserved along the timelike congruence represented by the
velocity of the dust fluid, leading to \emph{new} non-trivial constraints. This
fact has been used to conjecture that the resulting models correspond to the
spatially homogeneous (SH) models of Bianchi type I, at least for the case
where the cosmological constant vanish. By exploiting the full set of the
constraint equations as expressed in the 1+3 covariant formalism and using
elements from the theory of the spacelike congruences, we provide a direct and
simple proof of this conjecture for vacuum and dust fluid models, which shows
that the Szekeres family of solutions represents the most general class of SIIS
models. The suggested procedure also shows that, the uniqueness of the SIIS of
the Petrov type D is not, in general, affected by the presence of a non-zero
pressure fluid. Therefore, in order to allow a broader class of Petrov type I
solutions apart from the SH models of Bianchi type I, one should consider more
general ``silent'' configurations by relaxing the vanishing of the vorticity
and the magnetic part of the Weyl tensor but maintaining their ``silence''
properties i.e. the vanishing of the curls of and the pressure
.Comment: Latex, 19 pages, no figures;(v2) some clarification remarks and an
appendix are added; (v3) minor changes to match published versio
Comment on Ricci Collineations for type B warped space-times
We present two counterexamples to the paper by Carot et al. in Gen. Rel.
Grav. 1997, 29, 1223 and show that the results obtained are correct but not
general.Comment: LaTex, 3 pages, Eq. (9) and reference added, typos corrected; Gen.
Rel. Grav (to appear
Self-similar Bianchi models: II. Class B models
In a companion article (referred hearafter as paper I) a detailed study of
the simply transitive Spatially Homogeneous (SH) models of class A concerning
the existence of a simply transitive similarity group has been given. The
present work (paper II) continues and completes the above study by considering
the remaining set of class B models. Following the procedure of paper I we find
all SH models of class B subjected only to the minimal geometric assumption to
admit a proper Homothetic Vector Field (HVF). The physical implications of the
obtained geometric results are studied by specialising our considerations to
the case of vacuum and law perfect fluid models. As a result we
regain all the known exact solutions regarding vacuum and non-tilted perfect
fluid models. In the case of tilted fluids we find the \emph{general
}self-similar solution for the exceptional type VI model and we
identify it as equilibrium point in the corresponding dynamical state space. It
is found that this \emph{new} exact solution belongs to the subclass of models
, is defined for and
although has a five dimensional stable manifold there exist always two unstable
modes in the restricted state space. Furthermore the analysis of the remaining
types, guarantees that tilted perfect fluid models of types III, IV, V and
VII cannot admit a proper HVF strongly suggesting that these models either
may not be asymptotically self-similar (type V) or may be extreme tilted at
late times. Finally for each Bianchi type, we give the extreme tilted
equilibrium points of their state space.Comment: Latex, 15 pages, no figures; to appear in Classical Quantum Gravity
(uses iopart style/class files); (v2) minor corrections to match published
versio
Wave-like Solutions for Bianchi type-I cosmologies in 5D
We derive exact solutions to the vacuum Einstein field equations in 5D, under
the assumption that (i) the line element in 5D possesses self-similar symmetry,
in the classical understanding of Sedov, Taub and Zeldovich, and that (ii) the
metric tensor is diagonal and independent of the coordinates for ordinary 3D
space. These assumptions lead to three different types of self-similarity in
5D: homothetic, conformal and "wave-like". In this work we present the most
general wave-like solutions to the 5D field equations. Using the standard
technique based on Campbell's theorem, they generate a large number of
anisotropic cosmological models of Bianchi type-I, which can be applied to our
universe after the big-bang, when anisotropies could have played an important
role. We present a complete review of all possible cases of self-similar
anisotropic cosmologies in 5D. Our analysis extends a number of previous
studies on wave-like solutions in 5D with spatial spherical symmetry
A geometric description of the intermediate behaviour for spatially homogeneous models
A new approach is suggested for the study of geometric symmetries in general
relativity, leading to an invariant characterization of the evolutionary
behaviour for a class of Spatially Homogeneous (SH) vacuum and orthogonal
law perfect fluid models. Exploiting the 1+3 orthonormal frame
formalism, we express the kinematical quantities of a generic symmetry using
expansion-normalized variables. In this way, a specific symmetry assumption
lead to geometric constraints that are combined with the associated
integrability conditions, coming from the existence of the symmetry and the
induced expansion-normalized form of the Einstein's Field Equations (EFE), to
give a close set of compatibility equations. By specializing to the case of a
\emph{Kinematic Conformal Symmetry} (KCS), which is regarded as the direct
generalization of the concept of self-similarity, we give the complete set of
consistency equations for the whole SH dynamical state space. An interesting
aspect of the analysis of the consistency equations is that, \emph{at least}
for class A models which are Locally Rotationally Symmetric or lying within the
invariant subset satisfying , a proper KCS \emph{always
exists} and reduces to a self-similarity of the first or second kind at the
asymptotic regimes, providing a way for the ``geometrization'' of the
intermediate epoch of SH models.Comment: Latex, 15 pages, no figures (uses iopart style/class files); added
one reference and minor corrections; (v3) improved and extended discussion;
minor corrections and several new references are added; to appear in Class.
Quantum Gra
Self-similar Bianchi models: I. Class A models
We present a study of Bianchi class A tilted cosmological models admitting a
proper homothetic vector field together with the restrictions, both at the
geometrical and dynamical level, imposed by the existence of the simply
transitive similarity group. The general solution of the symmetry equations and
the form of the homothetic vector field are given in terms of a set of
arbitrary integration constants. We apply the geometrical results for tilted
perfect fluids sources and give the general Bianchi II self-similar solution
and the form of the similarity vector field. In addition we show that
self-similar perfect fluid Bianchi VII models and irrotational Bianchi
VI models do not exist.Comment: 14 pages, Latex; to appear in Classical and Quantum Gravit
On the general structure of Ricci collineations for type B warped spacetimes
A complete study of the structure of Ricci collineations for type B warped
spacetimes is carried out. This study can be used as a method to obtain these
symetries in such spacetimes. Special cases as 2+2 reducible spacetimes, and
plane and spherical symmetric spacetimes are considered specifically.Comment: 18 pages. Version accepted for publication in JM
Generalized Holographic Cosmology
We consider general black hole solutions in five-dimensional spacetime in the
presence of a negative cosmological constant. We obtain a cosmological
evolution via the gravity/gauge theory duality (holography) by defining
appropriate boundary conditions on a four-dimensional boundary hypersurface.
The standard counterterms are shown to renormalize the bare parameters of the
system (the four-dimensional Newton's constant and cosmological constant). We
discuss the thermodynamics of cosmological evolution and present various
examples. The standard brane-world scenarios are shown to be special cases of
our holographic construction.Comment: 15 pages, 5 figure
- …