Jaime F. Villas da Rocha

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.

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.

Constraining a double component dark energy model using supernova type Ia data

A two-component fluid representing dark energy is studied. One of the components has a polytropic form, while the other has a barotropic form. Exact solutions are obtained and the cosmological parameters are constrained using supernova type Ia data. In general, an open universe is predicted. A big rip scenario is largely preferred, but the dispersion in the parameter space is very high. Hence, even if scenarios without future singularities cannot be excluded with the allowed range of parameters, a phantom cosmology, with an open spatial section, is a general prediction of the model. For a wide range of the equation of state parameters there is an asymptotic de Sitter phase.

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

We study the evolution of an anisotropic fluid with kinematic self-similarity of the second kind. We found a class of solution to the Einstein field equations by assuming an equation of state where the radial pressure of the fluid is proportional to its energy density (pr = ωρ) and that the fluid moves along time-like geodesics. The self-similarity requires ω = -1. The energy conditions, geometrical and physical properties of the solutions are studied. We have found that, depending on the self-similar parameter α, they may represent a black hole or a naked singularity.

TYPE II FLUID SOLUTIONS TO EINSTEIN'S FIELD EQUATIONS IN N-DIMENSIONAL SPHERICAL SPACETIMES

A large class of Type II fluid solutions to Einstein field equations in N-dimensional spherical spacetimes is found, wich includes most of the known solutions. A family of the generalized collapsing Vaidya solutions with homothetic self-similarity, parametrized by a constant λ, is studied, and found that when λ>λc(N), the collapse always forms black holes, and when λ<λc(N), it always forms naked singularities, where λc(N) is function of the spacetime dimension N only.

GRAVITATIONAL COLLAPSE OF SPHERICALLY SYMMETRIC ANISOTROPIC FLUID WITH HOMOTHETIC SELF-SIMILARITY

We study spacetimes of spherically symmetric anisotropic fluid with homothetic self-similarity. We find a class of solutions to the Einstein field equations by assuming that the tangential pressure of the fluid is proportional to its radial one and that the fluid moves along time-like geodesics. The energy conditions, and geometrical and physical properties of these solutions are studied and found that some of them represent gravitational collapse of an anisotropic fluid.

PERTURBED SELF-SIMILAR MASSLESS SCALAR FIELD IN THE SPACE–TIMES WITH CIRCULAR SYMMETRY IN (2+1)-GRAVITY

We present in this work the study of the linear perturbations of the (2+1)-dimensional circularly symmetric solution, obtained in a previous work, with kinematic self-similarity of the second kind. We have obtained an exact solution for the perturbation equations and the possible perturbation modes. We have shown that the background solution is a stable solution.

Dressing a Naked Singularity: an Example

Considering the evolution of a perfect fluid with self-similarity of the second kind, we find that an initial naked singularity can be trapped by an event horizon due to collapsing matter. The fluid moves along timelike geodesics with a self-similar parameter α = -3. Since the metric obtained is not asymptotically flat, we match the space–time of the fluid with a Schwarzschild space–time. All the energy conditions are fulfilled until the naked singularity.

GRAVITATIONAL COLLAPSE OF MASSLESS SCALAR FIELD WITH NEGATIVE COSMOLOGICAL CONSTANT IN (2+1) DIMENSIONS

The 2+1-dimensional geodesic circularly symmetric solutions of Einstein-massless-scalar field equations with negative cosmological constant are found and their local and global properties are studied. It is found that one of them represents gravitational collapse where black holes are always formed.