Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Application of the Campbell-Magaard theorem to higher-dimensional
  physics   Stated succinctly, the original version of the Campbell-Magaard theorem says
that it is always possible to locally embed any solution of 4-dimensional
general relativity in a 5-dimensional Ricci-flat manifold. We discuss the proof
of this theorem (and its variants) in n dimensions, and its application to
current theories that postulate that our universe is a 4-dimensional
hypersurface Sigma_0 within a 5-dimensional manifold, such as Space-Time-Matter
(STM) theory and the Randall & Sundrum (RS) braneworld scenario. In particular,
we determine whether or not arbitrary spacetimes may be embedded in such
theories, and demonstrate how these seemingly disparate models are
interconnected. Special attention is given to the motion of test observers in 5
dimensions, and the circumstances under which they are confined to Sigma_0. For
each 5-dimensional scenario considered, the requirement that observers be
confined to the embedded spacetime places restrictions on the 4-geometry. For
example, we find that observers in the thin braneworld scenario can be
localized around the brane if its total stress-energy tensor obeys the
5-dimensional strong energy condition. As a concrete example of some of our
technical results, we discuss a Z_2 symmetric embedding of the standard
radiation-dominated cosmology in a 5-dimensional vacuum.

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The categories of this paper are: math
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: cs
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The categories of this paper are: supr-con