Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On "time-periodic" black-hole solutions to certain spherically symmetric
  Einstein-matter systems   This paper explores ``black hole'' solutions of various Einstein-wave matter
systems admitting an isometry of their domain of outer communications taking
every point to its future. In the first two parts, it is shown that such
solutions, assuming in addition that they are spherically symmetric and the
matter has a certain structure, must be Schwarzschild or Reissner-Nordstrom.
Non-trivial examples of matter for which the result applies are a wave map and
a massive charged scalar field interacting with an electromagnetic field. The
results thus generalize work of Bekenstein [1] and Heusler [12] from the static
to the periodic case. In the third part, which is independent of the first two,
it is shown that Dirac fields preserved by an isometry of a spherically
symmetric domain of outer communications of the type described above must
vanish. It can be applied in particular to the Einstein-Dirac-Maxwell equations
or the Einstein-Dirac-Yang/Mills equations, generalizing work of Finster,
Smoller, and Yau [9], [7], [8], and also [6].

28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
2
The categories of this paper are: math
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph