Bouncing compact objects. Part I. Quantum extension of the Oppenheimer-Snyder collapse

International audienceThis article proposes a generalization of the Oppenheimer-Snyder model which describes a bouncing compact object. The corrections responsible for the bounce are parameterized in a general way so as to remain agnostic about the specific mechanism of singularity resolution at play. It thus develops an effective theory based on a thin shell approach, inferring generic properties of such a UV complete gravitational collapse. The main result comes in the form of a strong constraint applicable to general UV models: if the dynamics of the collapsing star exhibits a bounce, it always occurs below, or at most at the energy threshold of horizon formation, so that only an instantaneous trapping horizon may be formed while a trapped region never forms. This conclusion relies solely on i) the assumption of continuity of the induced metric across the time-like surface of the star and ii) the assumption of a classical Schwarzschild geometry describing the (vacuum) exterior of the star. In particular, it is completely independent of the choice of corrections inside the star which leads to singularity-resolution. The present model provides thus a general framework to discuss bouncing compact objects, for which the interior geometry is modeled either by a classical or a quantum bounce. In the latter case, our no-go result regarding the formation of trapped region suggests that additional structure, such as the formation of an inner horizon, is needed to build consistent models of matter collapse describing black-to-white hole bounces. Indeed, such additional structure is needed to keep quantum gravity effects confined to the high curvature regime, in the deep interior region, providing thus a new challenge for current constructions of quantum black-to-white hole bounce models