  The gravitational collapse of a pressureless fluid in general relativity
(Oppenheimer-Snyder collapse) results in a black hole. The study of the same
phenomenon in the brane-world scenario has shown that the exterior of the
collapsing dust sphere cannot be static. We show that by allowing for pressure,
the exterior of a fluid sphere can be static. The gravitational collapse on the
brane proceeds according to the modified gravitational dynamics, turning the
initial nearly dust-like configuration into a fluid with tension. The tension
arises from the non-linearity of the dynamical equations in the energy-momentum
tensor, and it vanishes in the general relativistic limit. Below the horizon
the tension turns the star into dark energy. This transition occurs right below
the horizon for astrophysical black holes and far beyond the horizon for
intermediate mass and galactic black holes. Further, both the energy density
and the tension increase towards infinite values during the collapse. The
infinite tension however could not stop the formation of the singularity.
