Black holes and dark energy from gravitational collapse on the brane

TL;DR

This paper explores gravitational collapse on the brane, revealing that pressure allows for a static exterior and that the collapsing star can develop tension resembling dark energy, leading to singularities.

Contribution

It demonstrates that including pressure in brane-world collapse models permits static exteriors and introduces tension that transforms the star into dark energy near the horizon.

Findings

Exterior can be static with pressure

Tension arises from non-linearity in equations

Collapse leads to infinite tension and singularity

Abstract

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.