Considering charged fluid spheres as anisotropic sources and the diffusion limit as the transport mechanism, we suppose that the inner spacetime admits self-similarity. Matching the interior solution with the ReissnerNordström-Vaidya exterior one, we find an extremely compact and oscillatory final state with a redistribution of the electric charge function and non zero pressure profiles.

We incorporate a massless scalar field into a 3-dimensional code for the characteristic evolution of the gravitational field. The extended 3-dimensional code for the Einstein-Klein-Gordon system is calibrated to be second order convergent. It provides an accurate calculation of the gravitational and scalar radiation at infinity. As an application, we simulate the fully nonlinear evolution of an asymmetric scalar pulse of ingoing radiation propagating toward an interior Schwarzschild black hole and compute the backscattered scalar and gravitational outgoing radiation patterns. The amplitudes of the scalar and gravitational outgoing radiation modes exhibit the predicted power law scaling with respect to the amplitude of the initial data. For the scattering of an axisymmetric scalar field, the final ring down matches the complex frequency calculated perturbatively for the ℓ = 2 quasinormal mode.

We study the effect of transport processes ͑diffusion and free streaming͒ on a collapsing spherically symmetric distribution of matter in a self-similar space-time. A very simple solution shows interesting features when it is matched with the Vaidya exterior solution. In the mixed case ͑diffusion and free streaming͒, we find a barotropic equation of state in the stationary regime. In the diffusion approximation the gravitational potential at the surface is always constant; if we perturb the stationary state, the system is very stable, recovering the barotropic equation of state as time progresses. In the free-streaming case the self-similar evolution is stationary, but with a nonbarotropic equation of state.

We apply the postquasistatic approximation, an iterative method for the evolution of selfgravitating spheres of matter, to study the evolution of anisotropic non-adiabatic radiating and dissipative distributions in General Relativity. Dissipation is described by viscosity and free-streaming radiation, assuming an equation of state to model anisotropy induced by the shear viscosity. We match the interior solution, in non-comoving coordinates, with the Vaidya exterior solution. Two simple models are presented, based on the Schwarzschild and Tolman VI solutions, in the nonadiabatic and adiabatic limit. In both cases the eventual collapse or expansion of the distribution is mainly controlled by the anisotropy induced by the viscosity. PACS numbers: 04.25.-g,04.25.D-,0.40.-b

Unfortunately, several errors occurred in the published version of this article.• The affiliation of the corresponding author W. Barreto was incorrect. The correct information is given below. • In the 3 rd paragraph on p. 25 a wrong citation [35][36][37][38][39][40][41] was given. The complete paragraph with the correct citation is printed below:Few exact solutions to the Einstein-Maxwell equations are relevant to gravitational collapse. For this reason, new collapse solutions are very useful, even if they are simplified ones [31]. It is well known that the field equations admitThe online version of the original article can be found at http://dx