Seminar of Theory of Relativity and Gravitation

A black hole horizon is formed once a star collapses within its own Schwarzschild radius. After that, the collapsing matter reaches Planckian densities in a short proper time. What happens next is outside the reach of general relativity, as it involves the quantum behavior of the gravitational field in the strong field regime. Starting from the Oppenheimer-Snyder model, and considering quantum corrections coming from loop quantum gravity, I will show how the quantum-corrected Oppenheimer-Snyder model predicts a `bounce' of the collapsing star and a non-singular black hole interior where the trapped region smoothly transitions into the anti-trapped region of a white hole. The same qualitative bouncing physics is also present in the gravitational collapse of an inhomogeneous perfect fluid with pressure. However, in this scenario, the dynamics generally develops shell-crossing singularities, as in the classical theory. This shows that the mere inclusion of pressure and quantum gravitational effects is not able to resolve shell-crossing singularities. Finally, going back to the quantum-corrected Oppenheimer-Snyder model, I will comment on the quantum physics of the horizon of the black hole. If the evaporation process of the black hole is taken into account, its horizon will eventually reach Planckian size, where quantum gravitational effects can no longer be neglected. A natural assumption is then that, at this point, the horizon of the black hole undergoes a quantum transition from trapping to anti-trapping consistently with the transition of geometry taking place in the interior of the hole. In this scenario, known as the black-to-white hole transition, the black hole evolves into a white hole `remnant' living in the future of the parent black hole, in its same asymptotic region and location.