Can a variation of fine structure constant influence the fate of gravitational collapse?

We show that it is possible to steer clear of a spacetime singularity during gravitational collapse by considering 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. The 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 the theory for dimensional requirements.