Black holes and dark energy from gravitational collapse on the brane

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 nonlinearity 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.