Dynamical models of prototype gravastars are constructed and studied. The models are the Visser-Wiltshire three-layer gravastars, in which an infinitely thin spherical shell of a perfect fluid with the equation of state p = (1 − γ)σ divides the whole spacetime into two regions, where the internal region is de Sitter, and the external is Schwarzschild. When γ < 1 and Λ = 0, it is found that in some cases the models represent stable gravastars, and in some cases they represent "bounded excursion" stable gravastars, where the thin shell is oscillating between two finite radii, while in some other cases they collapse until the formation of black holes. However, when γ ≥ 1, even with Λ = 0, only black holes are found. In the phase space, the region for both stable gravastars and "bounded excursion" gravastars is very small in comparison to that of black holes, although it is not completely empty.

Here we generalized a previous model of gravastar consisted of an internal de Sitter spacetime, a dynamical infinitely thin shell with an equation of state, but now we consider an external de Sitter-Schwarzschild spacetime. We have shown explicitly that the final output can be a black hole, a "bounded excursion" stable gravastar, a stable gravastar, or a de Sitter spacetime, depending on the total mass of the system, the cosmological constants, the equation of state of the thin shell and the initial position of the dynamical shell. We have found that the exterior cosmological constant imposes a limit to the gravastar formation, i.e., the exterior cosmological constant must be smaller than the interior cosmological constant. Besides, we have also shown that, in the particular case where the Schwarzschild mass vanishes, no stable gravastar can be formed, but we still have formation of black hole.

In recent work we physically interpreted a special gravastar solution characterized by a zero Schwarzschild mass. In fact, in that case, none gravastar was formed and the shell expanded, leaving behind a de Sitter or a Minkowski spacetime, or collapsed without forming an event horizon, originating what we called a massive non-gravitational object. This object has two components of non zero mass but the exterior spacetime is Minkowski or de Sitter. One of the component is a massive thin shell and the other one is de Sitter spacetime inside. The total mass of this object is zero Schwarzschild mass, which characterizes an exterior vacuum spacetime. Here, we extend this study to the case where we have a charged shell. Now, the exterior is a Reissner-Nordström spacetime and, depending on the parameter ω = 1 − γ of the equation of state of the shell, and the charge, a gravastar structure can be formed. We have found that the presence of the charge contributes to the stability of the gravastar, if the charge is greater than a critical value. Otherwise, a massive non-gravitational object is formed for small charges.

Dynamical models of prototype gravastars made of phantom energy are constructed, in which an infinitely thin spherical shell of a perfect fluid with the equation of state p = (1 − γ)σ divides the whole spacetime into two regions, the internal region filled with a dark energy (or phantom) fluid, and the external Schwarzschild region. 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 or normal stars. In the phase space, the region for the "bounded excursion" gravastars is very small in comparison to that of black holes, but not empty, as found in our previous papers. Therefore, although the existence of gravastars can not be completely excluded from current analysis, the opposite is not possible either, that is, even if gravastars exist, they do not exclude the existence of black holes.

The Einstein–Aether (EA) theory belongs to a class of modified gravity theories characterized by the introduction of a time-like unit vector field called aether. In this scenario, a preferred frame arises as a natural consequence of a broken Lorentz invariance. In the present work, we have obtained and analyzed some exact solutions allowed by this theory for two particular cases of a perfect fluid, both with Friedmann–Lemaître–Robertson–Walker symmetry: (i) a fluid with constant energy density (p = –ρ0) and (ii) a fluid with zero energy density (ρ0 = 0) corresponding to the vacuum solution with and without cosmological constant (Λ), respectively. Our solutions show that the EA and general relativity (GR) theories only differ in coupling constants. This difference is clearly shown because of the existence of singularities that are not in GR theory. This characteristic appears in the solutions with p = –ρ0 as well as with ρ0 = 0, where this last one depends only on the aether field. Furthermore, we consider the term of the EA theory in the Raychaudhuri equation and discuss the meaning of the strong energy condition in this scenario and found that this depends on the aether field. The solutions admit an expanding or contracting system. Bounce, singular, constant, and accelerated expansion solutions were also obtained, exhibiting the richness of the EA theory from the dynamic point of view of a collapsing system or of a cosmological model. The analysis of energy conditions, considering an effective fluid, shows that the term of the aether contributes significantly for the accelerated expansion of the system for the case in which the energy density is constant. On the other hand, for the vacuum case (ρ0 = 0), the energy conditions are all satisfied for the aether fluid.