Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Proper time and length in Schwarzschild geometry   We study proper time ($\tau$) intervals for observers at rest in the universe
($U$) and anti-universe ($\bar{U}$) sectors of the Kruskal-Schwarzschild
eternal spacetime of mass $M$, and proper lengths ($\rho$) in the black hole
(BH) and white hole (WH) sectors. The fact that in asymptotically flat regions,
coordinate time $t$ at infinity is proper time, leads to a past directed
Kruskal time $T$ in $\bar{U}$. In the BH and WH sectors maximal proper lengths
coincide with maximal proper time intervals, $\pi M$, in these regions, i.e.
with the proper time of radial free falling (ejection) to (from) the
singularity starting (ending) from (at) rest at the horizon.

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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con