Evolving spheres of shear-free anisotropic fluid

The fluid models mentioned in the title are studied in a modified approach, based on two formulas for the mass function. All characteristics of the fluid are expressed through a master potential, satisfying an ordinary second order differential equation. Different constraints are imposed on this core of relations, finding new solutions and deriving the classical results for perfect fluids as particular cases. All charged anisotropic solutions, all conformally flat and all uniform density solutions are found. A large class of solutions with linear equation among the two pressures is derived, including the case of vanishing tangential pressure. The mechanism responsible for the appearance of equation of state is elucidated.Comment: 22 page

Algebraically special, expanding and twisting gravitational fields with vanishing NUT parameter

The system of Einstein-Maxwell equations for fields mentioned in the title is simplified. Known pure radiation solutions are systematized and new solutions are given by separating the variables.Comment: revte

A different approach to anisotropic spherical collapse with shear and heat radiation

In order to study the type of collapse, mentioned in the title, we introduce a physically meaningful object, called the horizon function. It directly enters the expressions for many of the stellar characteristics. The main junction equation, which governs the collapse, transforms into a Riccati equation with simple coefficients for the horizon function. We integrate this equation in the geodesic case. The same is done in the general case when one or another of the coefficients vanish. It is shown how to build classes of star models in this formulation of the problem and simple solutions are given.Comment: 15 pages, to appear in Int.J.Mod.Phys.