Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gravitational collapse and the formation of black holes for the
  spherically symmetric Einstein-Vlasov system   We review results on the spherically symmetric, asymptotically flat
Einstein-Vlasov system. We focus on a recent result where we found explicit
conditions on the initial data which guarantee the formation of a black hole in
the evolution. Among these data there are data such that the corresponding
solutions exist globally in Schwarzschild coordinates. We put these results
into a more general context, and we include arguments which show that the
spacetimes we obtain satisfy the weak cosmic censorship conjecture and contain
a black hole in the sense of suitable mathematical definitions of these
concepts which are available in the literature.

4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
2
The categories of this paper are: math
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys