Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Revisiting the Darmois and Lichnerowicz junction conditions   What have become known as the "Darmois" and "Lichnerowicz" junction
conditions are often stated to be equivalent, "essentially" equivalent, in a
"sense" equivalent, and so on. One even sees not infrequent reference to the
"Darmois-Lichnerowicz" conditions. Whereas the equivalence of these conditions
is manifest in Gaussian-normal coordinates, a fact that has been known for
close to a century, this equivalence does not extend to a loose definition of
"admissible" coordinates (coordinates in which the metric and its first order
derivatives are continuous). We show this here by way of a simple, but
physically relevant, example. In general, a loose definition of the
"Lichnerowicz" conditions gives additional restrictions, some of which simply
amount to a convenient choice of gauge, and some of which amount to real
physical restrictions, away from strict "admissible" coordinates. The situation
was totally confused by a very influential, and now frequently misquoted, paper
by Bonnor and Vickers, that erroneously claimed a proof of the equivalence of
the "Darmois" and "Lichnerowicz" conditions within this loose definition of
"admissible" coordinates. A correct proof, based on a strict definition of
"admissible" coordinates, was given years previous by Israel. It is that proof,
generally unrecognized, that we must refer to. Attention here is given to a
clarification of the subject, and to the history of the subject, which, it
turns out, is rather fascinating in itself.

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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: physics
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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: math-ph