On tilted perfect fluid Bianchi type VI0_0 self-similar models

We show that the tilted perfect fluid Bianchi VI$_0$ 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 $\gamma$ lies in the interval $(\frac 65,\frac 32)$. 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$_0$ models satisfying $n_\alpha ^\alpha =0$ 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 ($\mu$), the isotropic pressure ($p$), the heat flux $q^a$ and the traceless anisotropic pressure tensor $\pi_{ab}$. 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 $w=r^{2}-t^{2}$ 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