Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Formation of dynamically transversely trapping surfaces and the
  stretched hoop conjecture   A dynamically transversely trapping surface (DTTS) is a new concept of an
extension of a photon sphere that appropriately represents a strong gravity
region and has close analogy with a trapped surface. We study formation of a
marginally DTTS in time-symmetric, conformally flat initial data with two black
holes, with a spindle-shaped source, and with a ring-shaped source, and clarify
that $\mathcal{C}\lesssim 6\pi GM$ describes the condition for the DTTS
formation well, where $\mathcal{C}$ is the circumference and $M$ is the mass of
the system. This indicates that an understanding analogous to the hoop
conjecture for the horizon formation is possible. Exploring the ring system
further, we find configurations where a marginally DTTS with the torus topology
forms inside a marginally DTTS with the spherical topology, without being
hidden by an apparent horizon. There also exist configurations where a
marginally trapped surface with the torus topology forms inside a marginally
trapped surface with the spherical topology, showing a further similarity
between DTTSs and trapped surfaces.

10
The categories of this paper are: q-bio
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The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
2
The categories of this paper are: math
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom