Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Revisiting the Birkhoff theorem from a dual null point of view   The Birkhoff theorem is a well-known result in general relativity and it is
used in many applications. However, its most general version, due to Bona, is
almost unknown and presented in a form less accessible to the relativist and
cosmologist community. Moreover, many wield it mistakenly as a simple
transposition of Newton's iron sphere theorem. In the present work, we propose
a modern, dual null, presentation --- useful in many explorations, including
black holes --- of the theorem that renders accessible most of the results of
Bona's version. In addition, we discuss the fluid contents admissible for the
application of the theorem, beyond a vacuum, and we demonstrate how the
formalism greatly simplifies solving the dynamical equations and allows one to
express the solution as a power expansion in $r$. We present a family of
solutions that share the properties predicted by the Birkhoff theorem and
discuss the existence of trapped and antitrapped regions. The formalism
manifestly shows how the type of region --- trapped or untrapped --- determines
the character of the Killing vector.

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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: eess