The recent observations of gravitational waves from binary black hole mergers and of the ‘shadow’ of the supermassive black hole in the galaxy M87 have finally
delivered experimental data of phenomena where the limits of General Relativity could be tested. One one hand, observations seem to confirm that black hole
candidates are well described by the classical relativistic solutions. On the other hand, the existence of curvature singularities in such solutions suggests
that there must exist a regime where the classical description fails. Many theoretical models describing relativistic collapse without the occurrence of singularities have been developed over the last few decades. Such models may
bear significant consequences for astrophysical black holes. The times seem now mature enough to ask whether such consequences may be tested experimentally.