M. F. A. da Silva

On parameters of the Levi-Civita solution

The Levi-Civita (LC) solution is matched to a cylindrical shell of an anisotropic fluid. The fluid satisfies the energy conditions when the mass parameter is in the range . The mass per unit length of the shell is given explicitly in terms of , which has a finite maximum. The relevance of the results to the non-existence of horizons in the LC solution and to gauge cosmic strings is pointed out.

GRAVITATIONAL COLLAPSE OF SELF-SIMILAR AND SHEAR-FREE FLUID WITH HEAT FLOW

A class of solutions to Einstein field equations is studied, which represents gravitational collapse of thick spherical shells made of self-similar and shear-free fluid with heat flow. It is shown that such shells satisfy all the energy conditions, and the corresponding collapse always forms naked singularities.

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, from which 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 σ ≥ 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 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 choice of the free parameters involved in the solutions.

Star Models with Dark Energy

We have constructed star models consisting of four parts: (i) a homogeneous inner core with anisotropic pressure (ii) an infinitesimal thin shell separating the core and the envelope; (iii) an envelope of inhomogeneous density and isotropic pressure; (iv) an infinitesimal thin shell matching the envelope boundary and the exterior Schwarzschild spacetime. We have analyzed all the energy conditions for the core, envelope and the two thin shells. We have found that, in order to have static solutions, at least one of the regions must be constituted by dark energy. The results show that there is no physical reason to have a superior limit for the mass of these objects but for the ratio of mass and radius.

On Anisotropic Dark Energy Stars

Since the discovery of accelerated expansion of the universe, it was necessary to introduce a new component of matter distribution called dark energy. The standard cosmological model considers isotropy of the pressure and assumes an equation of state p = ωρ, relating the pressure p and the energy density ρ. The interval of the parameter ω defines the kind of matter of the universe, related to the fulfillment, or not, of the energy conditions of the fluid. The recent interest in this kind of fluid with anisotropic pressure, in the scenario of the gravitational collapse and star formation, imposes a careful analysis of the energy conditions and the role of the components of the pressure. Here, in this work, we show an example where the classification of dark energy for isotropic pressure fluids is used incorrectly for anisotropic fluids. The correct classification and its consequences are presented.

Anisotropic self-similar cosmological model with dark energy

We study space–times having spherically symmetric anisotropic fluid with self-similarity of zeroth kind. We find a class of solutions to the Einstein field equations by assuming a shear-free metric and that the fluid moves along time-like geodesics. The energy conditions, and geometrical and physical properties of the solutions are studied and we find that it can be considered as representing an accelerating universe. At the beginning all the energy conditions were fulfilled but beyond a certain time (a maximum geometrical radius) none of them is satisfied, characterizing a transition from normal matter (dark matter, baryon matter and radiation) to dark energy.

Topological charged black holes in high dimensional spacetimes and their formation from gravitational collapse of a type II fluid

Topological charged black holes coupled with a cosmological constant in

Levi-Cività solutions with a cosmological constant

{R}^{2}\ifmmode\times\else\texttimes\fi{}{X}^{D\ensuremath{-}2}

On the sources of static plane symmetric vacuum space-times

spacetimes are studied, where

GRAVITATIONAL COLLAPSE OF AN ANISOTROPIC FLUID WITH SELF-SIMILARITY OF THE SECOND KIND

{X}^{D\ensuremath{-}2}