Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of maximal hypersurfaces in some spherically symmetric
  spacetimes   We prove that the maximal development of any spherically symmetric spacetime
with collisionless matter (obeying the Vlasov equation) or a massless scalar
field (obeying the massless wave equation) and possessing a constant mean
curvature $S^1 \times S^2$ Cauchy surface also contains a maximal Cauchy
surface. Combining this with previous results establishes that the spacetime
can be foliated by constant mean curvature Cauchy surfaces with the mean
curvature taking on all real values, thereby showing that these spacetimes
satisfy the closed-universe recollapse conjecture. A key element of the proof,
of interest in itself, is a bound for the volume of any Cauchy surface $\Sigma$
in any spacetime satisfying the timelike convergence condition in terms of the
volume and mean curvature of a fixed Cauchy surface $\Sigma_0$ and the maximal
distance between $\Sigma$ and $\Sigma_0$. In particular, this shows that any
globally hyperbolic spacetime having a finite lifetime and obeying the
timelike-convergence condition cannot attain an arbitrarily large spatial
volume.

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The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
3
The categories of this paper are: physics
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg