We study the dynamical instability of a spherically symmetric anisotropic fluid which collapses adiabatically under the condition of vanishing expansion scalar. The Newtonian and post Newtonian regimes are considered in detail. It is shown that within those two approximations the adiabatic index Γ1, measuring the fluid stiffness, does not play any role. Instead, the range of instability is determined by the anisotropy of the fluid pressures and the radial profile of the energy density, independently of its stiffness, in a way which is fully consistent with results previously obtained from the study on the Tolman mass.

We study the dynamical instability of a spherically symmetric anisotropic fluid which collapses adiabatically under the condition of vanishing expansion scalar. The Newtonian and post Newtonian regimes are considered in detail. It is shown that within those two approximations the adiabatic index 1, measuring the fluid stiffness, does not play any role. Instead, the range of instability is determined by the anisotropy of the fluid pressures and the radial profile of the energy density, independently of its stiffness, in a way which is fully consistent with results previously obtained from the study on the Tolman mass.

We apply the thermodynamical model of the cosmological event horizon of the spatially flat FLRW metrics to the study of the recent accelerated expansion phase and to the coincidence problem. This model, called “ehT model” hereafter, led to a dark energy (DE) density Λ varying as r−2, where r is the proper radius of the event horizon. Recently, another model motivated by the holographic principle gave an independent justification of the same relation between Λ and r. We probe the theoretical results of the ehT model with respect to the SnIa observations and we compare it to the model deduced from the holographic principle, which we call “LHG model” in the following. Our results are in excellent agreement with the observations for H0=64kms−1Mpc−1, and ΩΛ0=0.63−0.01+0.1, which leads to q0=−0.445 and zT≃0.965.

We consider the evolution of cavities within spherically symmetric relativistic fluids, under the assumption that the proper radial distance between neighboring fluid elements remains constant during their evolution (purely areal evolution condition). The general formalism is deployed and solutions are presented. Some of them satisfy Darmois conditions whereas others present shells and must satisfy Israel conditions, on either one or both boundary surfaces. Prospective applications of these results to some astrophysical scenarios are suggested.

We study the dynamical instability of a spherically symmetric anisotropic fluid which collapses adiabatically under the condition of vanishing expansion scalar. The Newtonian and post Newtonian regimes are considered in detail. It is shown that within those two approximations the adiabatic index $\Gamma_1$, measuring the fluid stiffness, does not play any role. Instead, the range of instability is determined by the anisotropy of the fluid pressures and the radial profile of the energy density, independently of its stiffness, in a way which is fully consistent with results previously obtained from the study on the Tolman mass.

In a recent paper a systematic study on shearing expansion-free spherically symmetric distributions was presented. As a particular case of such systems, the Skripkin model was mentioned, which corresponds to a nondissipative perfect fluid with a constant energy density. Here we show that such a model is inconsistent with junction conditions. It is shown that in general for any nondissipative fluid distribution, the expansion-free condition requires the energy density to be inhomogeneous. As an example we consider the case of dust, which allows for a complete integration.

We present a complete set of the equations and matching conditions required for the description of physically meaningful charged, dissipative, spherically symmetric gravitational collapse with shear. Dissipation is described with both free-streaming and diffusion approximations. The effects of viscosity are also taken into account. The roles of different terms in the dynamical equation are analyzed in detail. The dynamical equation is coupled to a causal transport equation in the context of Israel-Stewart theory. The decrease of the inertial mass density of the fluid, by a factor which depends on its internal thermodynamic state, is reobtained, with the viscosity terms included. In accordance with the equivalence principle, the same decrease factor is obtained for the gravitational force term. The effect of the electric charge on the relation between the Weyl tensor and the inhomogeneity of energy density is discussed.

We consider a cosmological horizon, named thermo-horizon, to which are associated a temperature and an entropy of Bekenstein–Hawking and which obeys the first law for an energy flow calculated through the corresponding limit surface. We point out a contradiction between the first law and the definition of the total energy contained inside the horizon. This contradiction is removed when the first law is replaced by a Gibbs' equation for a vacuum-like component associated to the event horizon.

We present a complete set of the equations and matching conditions required for the description of physically meaningful charged, dissipative, spherically symmetric gravitational collapse with shear. Dissipation is described with both free-streaming and diffusion approximations. The effects of viscosity are also taken into account. The roles of different terms in the dynamical equation are analyzed in detail. The dynamical equation is coupled to a causal transport equation in the context of Israel-Stewart theory. The decrease of the inertial mass density of the fluid, by a factor which depends on its internal thermodynamic state, is reobtained, with the viscosity terms included. In accordance with the equivalence principle, the same decrease factor is obtained for the gravitational force term. The effect of the electric charge on the relation between the Weyl tensor and the inhomogeneity of the energy density is discussed.

We present the whole set of equations with regularity and matching conditions required for the description of physically meaningful static cylindrically symmmetric distributions of matter, smoothly matched to Levi-Civita vacuum spacetime. It is shown that the conformally flat solution with equal principal stresses represents an incompressible fluid. It is also proved that any conformally flat cylindrically symmetric static source cannot be matched through Darmois conditions to the Levi-Civita spacetime. Further evidence is given that when the Newtonian mass per unit length reaches 1/2, the spacetime has plane symmetry.

Here we study some general properties of spherical shear-free collapse. Its general solution when imposing conformal flatness is re-obtained (Refs. 1 and 2) and matched to the outgoing Vaidya spacetime. We propose a simple model satisfying these conditions and study its physical consequences. Special attention deserve, the role played by relaxational processes and the conspicuous link betweeen dissipation and density inhomogeneity.

We present the whole set of equations with regularity and matching conditions required for the description of physically meaningful static cylindrically symmmetric distributions of matter, smoothly matched to Levi-Civita vacuum spacetime. It is shown that the conformally flat solution with equal principal stresses represents an incompressible fluid. It is also proved that any conformally flat cylindrically symmetric static source cannot be matched through Darmois conditions to the Levi-Civita spacetime. Further evidence is given that when the Newtonian mass per unit length reaches 1/2 the spacetime has plane symmetry. e-mail: laherrera@telcel.net.ve e-mail: gele@ccr.jussieu.fr e-mail: santos@ccr.jussieu.fr and nos@cbpf.br

We investigate the temporal evolution of the redshift and the luminosity distance within the standard Friedmann-Roberston-Walker cosmological model. The redshift and luminosity distance of sources evolve with time and we show that they tend to given values, namely the stable equilibrium states associated to the first order differential equation they verify. This suggests that the sources concentrate at about these values. Furthermore, as these values depend only on the cosmological parameters, their measure could provide a new approach to determine the value of the cosmological constant.

Combining the second-order entropy flow vector of the causal Israel-Stewart theory with the conformal Killing-vector property of ui/T, where ui is the 4-velocity of the medium and T is its equilibrium temperature, we investigate generalized equilibrium states for cosmological fluids with non-conserved particle number. We calculate the corresponding equilibrium particle production rate and show that this quantity is reduced compared with the results of the previously studied first-order theory. Generalized equilibrium for massive particles turns out to be compatible with a dependence a-2 of the fluid energy density on the scale factor a of the Robertson-Walker metric and may be regarded as a realization of so-called K-matter.

We propose a new time evolution law for the cosmological `constant' in a spatially flat (k = 0) Friedmann-Lemaître-Robertson-Walker spacetime. From a thermodynamic model of the vacuum based upon work of Gibbons, Hawking and Davies, we obtain the law where r is the proper radius of the cosmological event horizon. From the field equations we can deduce a second-order differential equation for , that we solve numerically, showing that the cosmological `constant' problem could be solved phenomenologically. The decay of takes place during the deflationary era, and has the effect of creating a perfect fluid of strings. Finally, our model suggests a mechanism of destabilization of the de Sitter spacetime to explain the exit from inflation and the matter creation.

Recent calculations (analytical and semi-analytical), indicating that thermal effects in the relativistic regime may enhance the stability of spherically-symmetric models, are confirmed in a new example.

The present study of the space location of supernovae in their parent galaxies suggests a new method to obtain indicative values of the SN-galaxy center distances. This method is based on the use of the notions of ‘luminosity distance’ and ‘angular diameter distance’. On this account, it appears that one could avoid the corrections for the projection effect in no faced-on galaxies. In Section 2, a sample of 25 type I supernovae is treated at once by means of two distinct procedures: the one by Barbon, Capaccioli, and Ciatti, the one defined here. The good agreement of the results is shown, specially about the surface density of supernovae. In the last part, we try to test the influence of the internal obscuration of the SNs by their own galaxies, on the basis of a correction suggested by Nottale. The frequency distribution and the surface density of the objects of our sample support the consistency of such a correction.