  This 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 later
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.
