Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Volume Inside a Black Hole   The horizon (the surface) of a black hole is a null surface, defined by those
hypothetical "outgoing" light rays that just hover under the influence of the
strong gravity at the surface. Because the light rays are orthogonal to the
spatial 2-dimensional surface at one instant of time, the surface of the black
hole is the same for all observers (i.e. the same for all coordinate
definitions of "instant of time"). This value is 4*(pi)* (2Gm/c^2)^2 for
nonspinning black holes, with G= Newton's constant, c= speed of light, and m=
mass of the black hole.
  The 3-dimensional spatial volume inside a black hole, in contrast, depends
explicitly on the definition of time, and can even be time dependent, or zero.
We give examples of the volume found inside a standard, nonspinning spherical
black hole, for several different standard time-coordinate definitions.
Elucidating these results for the volume provides a new pedagogical resource of
facts already known in principle to the relativity community, but rarely worked
out.

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The categories of this paper are: math
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci