Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maxwell Fields in Spacetimes Admitting Non-Null Killing Vectors   We consider source-free electromagnetic fields in spacetimes possessing a
non-null Killing vector field, $\xi^a$. We assume further that the
electromagnetic field tensor, $F_{ab}$, is invariant under the action of the
isometry group induced by $\xi^a$. It is proved that whenever the two
potentials associated with the electromagnetic field are functionally
independent the entire content of Maxwell's equations is equivalent to the
relation $\n^aT_{ab}=0$. Since this relation is implied by Einstein's equation
we argue that it is enough to solve merely Einstein's equation for these
electrovac spacetimes because the relevant equations of motion will be
satisfied automatically. It is also shown that for the exceptional case of
functionally related potentials $\n^aT_{ab}=0$ implies along with one of the
relevant equations of motion that the complementary equation concerning the
electromagnetic field is satisfied.

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The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: math
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg