  We show that it is possible to steer clear of a spacetime singularity during
gravitational collapse by considering the time-variation of a fundamental
coupling, in this case, the fine structure constant {\alpha}. We study a
spherical distribution of cold dark matter coexisting with other fluid
elements, collapsing under its own gravity. Dark matter is written as a scalar
field interacting with electrically charged matter. This leads to a time
variation of {\alpha} and as a consequence, a breakdown of local charge
conservation within the sphere. The exterior has no such field and therefore,
Einstein's GR and standard equivalence principles remain valid. We derive the
lowest possible bound on the collapse of this sphere beyond which there is a
bounce and dispersal of most of the accumulated matter. We discuss the critical
behavior of the system around this point and show that the bound is connected
to a length scale of the order of Planck, introduced in theory for dimensional
requirements.

General Relativity and Quantum Cosmology;High Energy Physics - Theory