Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on the Penrose junction conditions   Impulsive pp-waves are commonly described either by a distributional
spacetime metric or, alternatively, by a continuous one. The transformation $T$
relating these forms clearly has to be discontinuous, which causes two basic
problems: First, it changes the manifold structure and second, the pullback of
the distributional form of the metric under $T$ is not well defined within
classical distribution theory. Nevertheless, from a physical point of view both
pictures are equivalent. In this work, after calculating $T$ als well as the
''Rosen''-form of the metric in the general case of a pp-wave with arbitrary
wave profile we give a precise meaning to the term ``physically equivalent'' by
interpreting $T$ as the distributional limit of a suitably regularized sequence
of diffeomorphisms. Moreover, it is shown that $T$ provides an example of a
generalized coordinate transformation in the sense of Colombeau's generalized
functions.

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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci