Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Type D Einstein spacetimes in higher dimensions   We show that all static spacetimes in higher dimensions are of Weyl types G,
I_i, D or O. This applies also to stationary spacetimes if additional
conditions are fulfilled, as for most known black hole/ring solutions. (The
conclusions change when the Killing generator becomes null, such as at Killing
horizons.) Next we demonstrate that the same Weyl types characterize warped
product spacetimes with a one-dimensional Lorentzian (timelike) factor, whereas
warped spacetimes with a two-dimensional Lorentzian factor are restricted to
the types D or O. By exploring the Bianchi identities, we then analyze the
simplest non-trivial case from the above classes - type D vacuum spacetimes,
possibly with a cosmological constant, dropping, however, the assumptions that
the spacetime is static, stationary or warped. It is shown that for ``generic''
type D vacuum spacetimes the corresponding principal null directions are
geodetic in any dimension (this applies also to type II spacetimes). For n>=5,
however, there may exist particular cases of type D spacetimes which admit
non-geodetic multiple principal null directions and we present such examples in
any n>=7. Further studies are restricted to five dimensions, where the type D
Weyl tensor is described by a 3x3 matrix \Phi_{ij}. In the case with
``twistfree'' (A_{ij}=0) principal null geodesics we show that in a ``generic''
case \Phi_{ij} is symmetric and eigenvectors of \Phi_{ij} coincide with those
of the expansion matrix S_{ij}, providing us with three preferred spacelike
directions of the spacetime. Similar results are also obtained when relaxing
the twistfree condition and assuming instead that \Phi_{ij} is symmetric. The
n=5 Myers-Perry black hole and Kerr-NUT-AdS metrics in arbitrary dimension are
briefly studied as specific examples of type D vacuum spacetime.

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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph