Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the formation of trapped surfaces   In a recent important breakthrough D. Christodoulou has solved a long
standing problem of General Relativity of evolutionary formation of trapped
surfaces in the Einstein-vacuum space-times. He has identified an open set of
regular initial conditions on an outgoing null hypersurface (both finite and at
past null infinity) leading to a formation a trapped surface in the
corresponding vacuum space-time to the future of the initial outgoing
hypersurface and another incoming null hypersurface with the prescribed
Minkowskian data.
  In this paper we give a simpler proof for a finite problem by enlarging the
admissible set of initial conditions and, consistent with this, relaxing the
corresponding propagation estimates just enough that a trapped surface still
forms. We also reduce the number of derivatives needed in the argument from two
derivatives of the curvature to just one. More importantly, the proof, which
can be easily localized with respect to angular sectors, has the potential for
further developments.

20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn