The asymptotic behaviour in Schwarzschild time of Vlasov matter in spherically symmetric gravitational collapse

• Given a static Schwarzschild spacetime of ADM mass M, it is well known that no ingoing causal geodesic starting in the outer domain r > 2M will cross the event horizon r = 2M in finite Schwarzschild time. We show that in gravitational collapse of Vlasov matter this behaviour can be very different. We construct initial data for which a black hole forms and all matter crosses the event horizon as Schwarzschild time goes to infinity, and show that this is a necessary condition for geodesic completeness of the event horizon. In addition to a careful analysis of the asymptotic behaviour of the matter characteristics our proof requires a new argument for global existence of solutions to the spherically symmetric Einstein–Vlasov system in an outer domain, since our initial data have non-compact support in the radial momentum variable and previous methods break down.

Ämnesord

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

NATURVETENSKAP  -- Fysik -- Astronomi, astrofysik och kosmologi (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences -- Astronomy, Astrophysics and Cosmology (hsv//eng)

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