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It is well known that the concept of black hole has been considered veryfascinating by scientists even before the introduction of Einstein's generalrelativity. They should be the final result of an irreversible gravitationalcollapse of very massive bodies. However, an unsolved problem concerning suchobjects is the presence of a space-time singularity in their core. Such aproblem was present starting by the first historical papers concerning blackholes. It is a common opinion that this problem could be solved when a correctquantum gravity theory will be, finally, constructed. In this work we review away to remove black hole singularities at a classical level i.e. withoutarguments of quantum gravity. By using a particular non-linear electrodynamicsLagrangian, an exact solution of Einstein field equations is shown. Thesolution prevents the collapsing object to reach the gravitational radius, thusthe final result becomes a black star, i.e. an astrophysical object where bothof singularities and event horizons are removed. Such solution is not only amathematical artifice. In fact, this kind of Lagrangian has been recently usedin various analysis in astrophysics, like surface of neutron stars and pulsars.The authors also recently adapted the analysis on a cosmological context byshowing that the big-bang singularity can be removed too.

Irreversible gravitational collapse: black stars or black holes?