Classification of Oppenheimer-Snyder Collapse: Singular, Bouncing, and Soft-Landing Scenarios

We study Oppenheimer-Snyder (OS) gravitational collapse matched to a general static, spherically symmetric exterior spacetime. Unlike the Schwarzschild case, two new features can arise in black holes with two horizons: an apparent-horizon left vertex, a temporary minimum in the apparent-horizon radius during collapse, and a bounce, where the star surface stops collapsing at a nonzero radius and reverses into expansion. We identify the conditions that lead to these two features. For two-horizon exteriors, trapped-region consistency requires that the apparent-horizon turning point occurs no earlier than the surface crossing of the inner horizon. As a concrete example, the OS collapse of the Reissner-Nordstr\"om (RN) spacetime shows both effects. In contrast, regular black holes with de Sitter cores show neither: their collapse is smooth and monotonic, and the surface approaches the center only as the proper time goes to infinity. These results naturally classify the OS collapses into three categories: singular, which ends at the center in finite time; bouncing, which reverses at a finite radius; and soft-landing, which reaches the center only asymptotically. We argue that these features are consistent with Penrose's strong cosmic censorship conjecture.