Gravitational Collapse of Circularly Symmetric Stiff Fluid with Self-Similarity in 2+1 Gravity

Linear perturbations of homothetic self-similar stiff fluid solutions, $S[n]$, with circular symmetry in 2+1 gravity are studied. It is found that, except for those with $n = 1$ and $n = 3$, none of them is stable and all have more than one unstable mode. Hence, {\em none of these solutions can be critical}.Comment: latex file, 1 figure; last version to appear in Prog. Theor. Phy

Fractals and the Distribution of Galaxies

This paper presents a review of the fractal approach for describing the large scale distribution of galaxies. We start by presenting a brief, but general, introduction to fractals, which emphasizes their empirical side and applications rather than their mathematical side. Then we discuss the standard correlation function analysis of galaxy catalogues and many observational facts that brought increasing doubts about the reliability of this method, paying special attention to the standard analysis implicit assumption of an eventual homogeneity of the distribution of galaxies. Some new statistical concepts for analysing this distribution is presented, and without the implicit assumption of homogeneity they bring support to the hypothesis that the distribution of galaxies does form a fractal system. The Pietronero-Wertz's single fractal (hierarchical) model is presented and discussed, together with the implications of this new approach for understanding galaxy clustering

Probing the stability of gravastars by dropping dust shells onto them

As a preparation for the dynamical investigations, this paper begins with a short review of the three-layer gravastar model with distinguished attention to the structure of the pertinent parameter space of gravastars in equilibrium. Then the radial stability of these types of gravastars is studied by determining their response for the totally inelastic collision of their surface layer with a dust shell. It is assumed that the dominant energy condition holds and the speed of sound does not exceed that of the light in the matter of the surface layer. While in the analytic setup the equation of state is kept to be generic, in the numerical investigations three functionally distinct classes of equations of states are applied. In the corresponding particular cases the maximal mass of the dust shell that may fall onto a gravastar without converting it into a black hole is determined. For those configurations which remain stable the excursion of their radius is assigned. It is found that even the most compact gravastars cannot get beyond the lower limit of the size of conventional stars, provided that the dominant energy condition holds in both cases. It is also shown---independent of any assumption concerning the matter interbridging the internal de Sitter and the external Schwarzschild regions---that the better is a gravastar in mimicking a black hole the easier is to get the system formed by a dust shell and the gravastar beyond the event horizon of the composite system. In addition, a generic description of the totally inelastic collision of spherical shells in spherically symmetric spacetimes is also provided in the appendix.Comment: 29 pages, 10 figure

Levi-Civita Solutions Coupled with Electromagnetic Fields

The local and global properties of the Levi-Civita (LC) solutions coupled with an electromagnetic field are studied and some limits to the vacuum LC solutions are given. By doing such limits, the physical and geometrical interpretations of the free parameters involved in the solutions are made clear. Sources for both the LC vacuum solutions and the LC solutions coupled with an electromagnetic field are studied, and in particular it is found that all the LC vacuum solutions with $\sigma \ge 0$ can be produced by cylindrically symmetric thin shells that satisfy all the energy conditions, weak, dominant, and strong. When the electromagnetic field is present, the situation changes dramatically. In the case of a purely magnetic field, all the solutions with $\sigma \ge 1/\sqrt{8}$ or $\sigma \le - 1/\sqrt{8}$ can be produced by physically acceptable cylindrical thin shells, while in the case of a purely electric field, no such shells are found for any value of $\sigma$.Comment: Typed in Revtex, including two figure

Bounded excursion stable gravastars and black holes

Dynamical models of prototype gravastars were constructed in order to study their stability. The models are the Visser-Wiltshire three-layer gravastars, in which an infinitely thin spherical shell of stiff fluid divides the whole spacetime into two regions, where the internal region is de Sitter, and the external is Schwarzschild. It is found that in some cases the models represent the "bounded excursion" stable gravastars, in which the thin shell is oscillating between two finite radii, while in other cases they collapse until the formation of black holes. In the phase space, the region for the ``bounded excursion" gravastars is very small in comparison to that of black holes, but not empty. Therefore, although the existence of gravastars cannot be excluded from such dynamical models, our results do indicate that, even if gravastars indeed exist, they do not exclude the existence of black holes.Comment: Revtex4, 12 figures. Version published in JCAP, 06 (2008) 02

Bounded excursion stable gravastars and black holes

International audienceDynamical models of prototype gravastars were constructed in order to study their stability. The models are the Visser-Wiltshire three-layer gravastars, in which an infinitely thin spherical shell of stiff fluid divides the whole spacetime into two regions, where the internal region is de Sitter, and the external one is Schwarzschild. It is found that in some cases the models represent the 'bounded excursion' stable gravastars, where the thin shell is oscillating between two finite radii, while in other cases they collapse until the formation of black holes occurs. In the phase space, the region for the 'bounded excursion' gravastars is very small in comparison to that of black holes, but not empty. Therefore, although the possibility of the existence of gravastars cannot be excluded from such dynamical models, our results indicate that, even if gravastars do indeed exist, that does not exclude the possibility of the existence of black holes