Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rigidity of marginally outer trapped 2-spheres   In a recent work, Galloway [9] proved a local foliation theorem by MOTSs for
a 3-dimensional initial data set $(M,g,K)$ with mean curvature $\tau\le0$ in a
4-dimensional spacetime $(\overline M,\overline g)$ when (under suitable
assumptions) $M$ has a stable spherical MOTS $\Sigma$ which achieves an upper
bound for the area. He proved that each leaf is a round 2-sphere with the same
constant Gaussian curvature. Here, we improve his result by dropping the
hypothesis on the mean curvature of $M$ and showing that each leaf is a minimal
surface. We show that in an outer neighborhood $U$ of $\Sigma$, the metric $g$
splits as the product $([0,\varepsilon)\times\Sigma,dt^2+g_0)$, where
$(\Sigma,g_0)$ is a round 2-sphere. In fact, we prove that the outer
neighborhood $U$ can be isometrically embedded into the 4-dimensional Nariai
spacetime $(\overline N,\overline h)$ as a spacelike hypersurface so that
$g|_U$ is the induced metric from $\overline N$ and $K|_U$ is the second
fundamental form of $U$ in $\overline N$. This completely classifies the local
geometry of such initial data sets.

9
The categories of this paper are: nlin
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex