Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the initial boundary value problem for the vacuum Einstein equations
  and geometric uniqueness   We formulate a well-posed initial boundary value problem (IBVP) for the
vacuum Einstein equations in harmonic gauge by describing the boundary
conditions of a spacetime metric in its associated gauge. This gauge is
determined, equivariantly with respect to diffeomorphisms, by the spacetime
metric. Further we show that vacuum spacetimes satisfying fixed
initial-boundary conditions and corner conditions are geometrically unique near
the initial surface. In analogy to the solution to the Cauchy problem, we also
construct a unique maximal globally hyperbolic vacuum development of the
initial-boundary data.

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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
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The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: astro-ph