We study the evolution of an anisotropic shear-free fluid with heat flux and kinematic self-similarity of the second kind. We found a class of solution to the Einstein field equations by assuming that the part of the tangential pressure which is expl
icitly time dependent of the fluid is zero and that the fluid moves along time-like geodesics. The energy conditions, geometrical and physical properties of the solutions are studied. The energy conditions are all satisfied at the beginning of the collapse but when the system approaches the singularity the energy conditions are violated, allowing for the appearance of an attractive phantom energy. We have found that, depending on the self-similar parameter $alpha$ and the geometrical radius, they may represent a naked singularity. We speculate that the apparent horizon disappears due to the emergence of exotic energy at the end of the collapse, or due to the characteristics of null acceleration systems as shown by recent work.
We investigate the geodesics kinematics and dynamics in the Linet-Tian metric with Lambda<0 and compare with the results for the Levi-Civita metric, when Lambda=0. This is used to derive new stability results about the geodesics dynamics in static va
cuum cylindrically symmetric spacetimes with respect to the introduction of Lambda<0. In particular, we find that increasing |Lambda| always increases the minimum and maximum radial distances to the axis of any spatially confined planar null geodesic. Furthermore, we show that, in some cases, the inclusion of any Lambda<0 breaks the geodesics orbit confinement of the Lambda=0 metric, for both planar and non-planar null geodesics, which are therefore unstable. Using the full system of geodesics equations, we provide numerical examples which illustrate our results.
We investigate the matching, across cylindrical surfaces, of static cylindrically symmetric conformally flat spacetimes with a cosmological constant $Lambda$, satisfying regularity conditions at the axis, to an exterior Linet-Tian spacetime. We prove
that for $Lambdaleq 0$ such matching is impossible. On the other hand, we show through simple examples that the matching is possible for $Lambda>0$. We suggest a physical argument that might explain these results.
We consider a gravastar model made of anisotropic dark energy with an infinitely thin spherical shell of a perfect fluid with the equation of state $p = (1-gamma)sigma$ with an external de Sitter-Schwarzschild region. It is found that in some cases t
he 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 or naked singularities. An interesting result is that we can have black hole and stable gravastar formation even with an interior and a shell constituted of dark and repulsive dark energy, as also shown in previous work. Besides, in three cases we have a dynamical evolution to a black hole (for $Lambda=0$) or to a naked singularity (for $Lambda > 0$). This is the first time in the literature that a naked singularity emerges from a gravastar model.
We consider a gravastar model made of anisotropic dark energy with an infinitely thin spherical shell of a perfect fluid with the equation of state $p = (1-gamma)sigma$ with an external de Sitter-Schwarzschild region. It is found that in some cases t
he 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 or naked singularities. An interesting result is that we can have black hole and stable gravastar formation even with an interior and a shell cons tituted of dark and repulsive dark energy, as also shown in previous work. Besides, in one case we have a dynamical evolution to a black hole (for $Lambda =0$) or to a naked singularity (for $Lambda > 0$). This is the first time in the literature that a naked singularity emerges from a gravastar model.
This investigation is devoted to the solutions of Einsteins field equations for a circularly symmetric anisotropic fluid, with kinematic self-similarity of the first kind, in $(2+1)$-dimensional spacetimes. In the case where the radial pressure vanis
hes, we show that there exists a solution of the equations that represents the gravitational collapse of an anisotropic fluid, and this collapse will eventually form a black hole, even when it is constituted by the phantom energy.
Considering the evolution of a perfect fluid with self-similarity of the second kind, we have found that an initial naked singularity can be trapped by an event horizon due to collapsing matter. The fluid moves along time-like geodesics with a self-s
imilar parameter $alpha = -3$. Since the metric obtained is not asymptotically flat, we match the spacetime of the fluid with a Schwarzschild spacetime. All the energy conditions are fulfilled until the naked singularity.
Since the discovery of the 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 s
tate $p=omega rho$, relating the pressure $p$ and the energy density $rho$. The interval of the parameter $omega$ 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 carefull 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.
