On gravitational collapse and integrable singularities

Schwarzschild black holes are expected to emerge as the end states of the classical gravitational collapse from non-singular configurations. After integrable curvature singularities appear, the interior geometry can be modelled to exhibit a transition, called “Minkowski breaking”, when the inner horizon disappears, before all matter collapses into the central singularity. This picture implies a quantum frame- work to describe the final stages of the gravitational collapse, and here we will provide more insights from the semiclassi- cal approximation for the energy–momentum tensor and the Madelung approximation for collapsing matter. In particular, we will show that the quantum potential in the Raychaud- huri equation starts to strongly oppose the collapse towards the Schwarzschild singularity precisely after the Minkowski breaking.