  The general exact solution of the Einstein-matter field equations describing
spherically symmetric shells satisfying an equation of state in closed form is
discussed under general assumptions of physical reasonableness. The solutions
split into two classes: a class of "astro-physically interesting" solutions
describing "ordinary" matter with positive density and pressure, and a class of
"phantom-like" solutions with positive density but negative active
gravitational mass, which can also be of interest in several "very strong
fields" regimes. Known results on linear-barotropic equations of state are
recovered as particular cases.
