47 research outputs found
On tilted perfect fluid Bianchi type VI self-similar models
We show that the tilted perfect fluid Bianchi VI family of self-similar
models found by Rosquist and Jantzen [K. Rosquist and R. T. Jantzen, \emph{%
Exact power law solutions of the Einstein equations}, 1985 Phys. Lett.
\textbf{107}A 29-32] is the most general class of tilted self-similar models
but the state parameter lies in the interval .
The model has a four dimensional stable manifold indicating the possibility
that it may be future attractor, at least for the subclass of tilted Bianchi
VI models satisfying in which it belongs. In addition
the angle of tilt is asymptotically significant at late times suggesting that
for the above subclasses of models the tilt is asymptotically extreme.Comment: Latex, 7 pages, no figures; (v2) some clarification comments are
added in the discussion and one reference; (v3) minor corrections in
equations (1), (3) and (19
Geometric equations of state in Friedmann-Lema\^{i}tre universes admitting matter and Ricci Collineations
As a rule in General Relativity the spacetime metric fixes the Einstein
tensor and through the Field Equations (FE) the energy-momentum tensor. However
one cannot write the FE explicitly until a class of observers has been
considered. Every class of observers defines a decomposition of the
energy-momentum tensor in terms of the dynamical variables energy density
(), the isotropic pressure (), the heat flux and the traceless
anisotropic pressure tensor . The solution of the FE requires
additional assumptions among the dynamical variables known with the generic
name equations of state. These imply that the properties of the matter for a
given class of observers depends not only on the energy-momentum tensor but on
extra a priori assumptions which are relevant to that particular class of
observers. This makes difficult the comparison of the Physics observed by
different classes of observers for the {\it same} spacetime metric. One way to
overcome this unsatisfactory situation is to define the extra condition
required among the dynamical variables by a geometric condition, which will be
based on the metric and not to the observers. Among the possible and multiple
conditions one could use the consideration of collineations. We examine this
possibility for the Friedmann-Lema\^{i}tre-Robertson-Walker models admitting
matter and Ricci collineations and determine the equations of state for the
comoving observers. We find linear and non-linear equations of state, which
lead to solutions satisfying the energy conditions, therefore describing
physically viable cosmological models.Comment: 14 pages, Latex; to appear in General Relativity and Gravitatio
Constructing a family of conformally flat scalar field models
Using purely geometrical methods we solve analytically the scalar field
equations of motion in a spherically symmetric background and found the
\emph{complete} set of scalar field (minimally coupled with gravity) spacetimes
which are of Petrov type O (conformally flat) and admit a \emph{gradient}
Conformal Vector Field. It is shown that the full group of scalar field
equations reduced to a \emph{single} equation that depends only on the distance
leaving the metric function freely chosen. We provide
physically sound examples and prove that (A)deSitter spacetime fits to this
scheme. We also reconstruct a recently found solution \cite% {Strumia:2022kez}
representing an expanding scalar bubble with Schwarzschild-like behaviour.Comment: 7 pages, no figures, uses iop class style; (v2) minor typos correcte