We discuss the equilibrium conditions of the gravitational collapse of a
spherically symmetric matter cloud. We analyze the spinor structure of a
general collapsing space-time and redefine the equilibrium conditions by using
Cartan scalars. We qualitatively investigate the equilibrium configuration of a
two-fluid system consisting of a dust-like fluid and a fluid with a negative
equation of state. We use our results to investigate certain cosmological
scenarios where dark energy can cluster inside the over-dense regions of dark
matter and together reaches a stable configuration. We compare the outcomes of
our work with existing work where the virialization technique is used to
stabilize the two-fluid system.Comment: 20 pages, 7 figure