Treffer: Black Hole Formation from a Complete Regular Past for Collisionless Matter

Initial data for the spherically symmetric Einstein―Vlasov system is constructed whose past evolution is regular and whose future evolution contains a black hole. This is the first example of initial data with these properties for the Einstein-matter system with a realistic matter model. One consequence of the result is that there exists a class of initial data for which the ratio of the Hawking mass m= m(r) and the area radius r is arbitrarily small everywhere, such that a black hole forms in the evolution. This result is in a sense analogous to the result (Christodoulou Commun Pure Appl Math 44:339―373, 1991) for a scalar field. Another consequence is that there exist black hole initial data such that the solutions exist for all Schwarzschild time t ∈ (―∞,∞).