  Gravitational collapse singularities are undesirable, yet inevitable to a
large extent in General Relativity. When matter satisfying null energy
condition collapses to the extent a closed trapped surface is formed, a
singularity is inevitable according to Penrose's singularity theorem. Since
positive mass vacuum solutions are generally black holes with trapped surfaces
inside the event horizon, matter cannot collapse to an arbitrarily small size
without generating a singularity. However, in modified theories of gravity
where positive mass vacuum solutions are naked singularities with no trapped
surfaces, it is reasonable to expect that matter can collapse to an arbitrarily
small size without generating a singularity. Here we examine this possibility
in the context of a modified theory of gravity with torsion in an extra
dimension. We study singularity-free static shell solutions to evaluate the
validity of the null energy condition on the shell. We find that with
sufficiently high pressure, matter can be collapsed to arbitrarily small size
without violating the null energy condition and without producing a
singularity.
