In Section 3.7 we discuss results on the formation of black holes and trapped surfaces; in particular,
the results in [20] will be presented. A corollary of the main result in [20
] concerns the issue
of global existence and thus we mention it here. It is shown that a particular class of initial
data, which lead to formation of black holes, have the property that the solutions exist for all
Schwarzschild time. The initial data consist of two parts: an inner part, which is a static solution of the
Einstein–Vlasov system, and an outer part with matter moving inwards. The set-up is shown to
preserve the direction of the momenta of the outer part of the matter, and it is also shown that in
Schwarzschild time the inner part and the outer part of the matter never interact in Schwarzschild
time.
http://www.livingreviews.org/lrr-2011-4 |
Living Rev. Relativity 14, (2011), 4
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