Qualitative analysis of collapsing isotropic fluid spacetimes

The structure of the Einstein field equations describing the gravitational collapse of spherically symmetric isotropic fluids is analyzed here for general equations of state. A suitable system of coordinates is constructed which allows us, under a hypothesis of Taylor-expandability with respect to one of the coordinates, to approach the problem of the nature of the final state without knowing explicitely the metric. The method is applied to investigate the singularities of linear barotropic perfect fluids solutions and to a family of accelerating fluids.