Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A class of dust-like self-similar solutions of the massless
  Einstein-Vlasov system   In this paper the existence of a class of self-similar solutions of the
Einstein-Vlasov system is proved. The initial data for these solutions are not
smooth, with their particle density being supported in a submanifold of
codimension one. They can be thought of as intermediate between smooth
solutions of the Einstein-Vlasov system and dust. The motivation for studying
them is to obtain insights into possible violation of weak cosmic censorship by
solutions of the Einstein-Vlasov system. By assuming a suitable form of the
unknowns it is shown that the existence question can be reduced to that of the
existence of a certain type of solution of a four-dimensional system of
ordinary differential equations depending on two parameters. This solution
starts at a particular point $P_0$ and converges to a stationary solution $P_1$
as the independent variable tends to infinity. The existence proof is based on
a shooting argument and involves relating the dynamics of solutions of the
four-dimensional system to that of solutions of certain two- and
three-dimensional systems obtained from it by limiting processes.

12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
2
The categories of this paper are: math
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph