Evolution of relativistic polytropes in the post--quasi--static regime

A recently presented method for the study of evolving self-gravitating relativistic spheres is applied to the description of the evolution of relativistic polytropes. Two different definitions of relativistic polytrope, yielding the same Newtonian limit, are considered. Some examples are explicitly worked out, describing collapsing polytropes and bringing out the differences between both types of polytropes.Comment: 42 pages, 7 figures; accepted for publication in GR

Heat flow in the postquasistatic approximation

We apply the postquasistatic approximation to study the evolution of spherically symmetric fluid distributions undergoing dissipation in the form of radial heat flow. For a model which corresponds to an incompressible fluid departing from the static equilibrium, it is not possible to go far from the initial state after the emission of a small amount of energy. Initially collapsing distributions of matter are not permitted. Emission of energy can be considered as a mechanism to avoid the collapse. If the distribution collapses initially and emits one hundredth of the initial mass only the outermost layers evolve. For a model which corresponds to a highly compressed Fermi gas, only the outermost shell can evolve with a shorter hydrodynamic time scale.Comment: 5 pages, 5 figure