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 mIS= mIS (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 .

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

einstein-vlasov system

gravitational collapse

steady-states

singularities

existence

einstein-vlasov system

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