Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic Behaviour of the Proper Length and Volume of the
  Schwarzschild Singularity   Though popular presentations give the Schwarzschild singularity as a point it
is known that it is spacelike and not timelike. Thus it has a "length" and is
not a "point". In fact, its length must necessarily be infinite. It has been
proved that the proper length of the Qadir-Wheeler suture model goes to
infinity [1], while its proper volume shrinks to zero, and the asymptotic
behaviour of the length and volume have been calculated. That model consists of
two Friedmann sections connected by a Schwarzschild "suture". The question
arises whether a similar analysis could provide the asymptotic behaviour of the
Schwarzschild black hole near the singularity. It is proved here that, unlike
the behaviour for the suture model, for the Schwarzschild essential singularity
$\Delta s$ $\thicksim $ $K^{1/3}\ln K$ and $V\thicksim $ $K^{-1}\ln K$, where
$K$ is the mean extrinsic curvature, or the York time.

31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
2
The categories of this paper are: math
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: stat