Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Bondi-Sachs metric at the vertex of a null cone: axially symmetric
  vacuum solutions   In the Bondi-Sachs formulation of General Relativity space-time is foliated
via a family of null cones. If these null cones are defined such that their
vertices are traced by a regular world-line then the metric tensor has to obey
regularity conditions at the vertices. We explore these regularity conditions
when the world line is a time-like geodesic. In particular, we solve the
Einstein equations for the Bondi-Sachs metric near the vertices for axially
symmetric vacuum space- times. The metric is calculated up to third order
corrections with respect to a flat metric along the time-like geodesic, as this
is the lowest order where non- linear coupling of the metric coefficients
occurs. We also determine the boundary conditions of the metric to arbitrary
order of these corrections when a linearized and axially symmetric vacuum
space-time is assumed. In both cases we find that (i) the initial data on the
null cone must have a very rigid angular structure for the vertex to be a
regular point, and (ii) the initial data are determined by functions depending
only on the time of a geodesic observer tracing the vertex. The latter
functions can be prescribed freely, but if the vertex is assumed to be regular
they must be finite and have finite derivatives along the geodesic.

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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: math
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas