Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Moduli space of stationary vacuum black holes from integrability   We consider the classification of asymptotically flat, stationary, vacuum
black hole spacetimes in four and five dimensions, that admit one and two
commuting axial Killing fields respectively. It is well known that the Einstein
equations reduce to a harmonic map on the two-dimensional orbit space, which
itself arises as the integrability condition for a linear system of spectral
equations. We integrate the Belinski-Zakharov spectral equations along the
boundary of the orbit space and use this to fully determine the metric and
associated Ernst and twist potentials on the axes and horizons. This is
sufficient to derive the moduli space of solutions that are free of conical
singularities on the axes, for any given rod structure. As an illustration of
this method we obtain constructive uniqueness proofs for the Kerr and
Myers-Perry black holes and the known doubly spinning black rings.

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The categories of this paper are: supr-con
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The categories of this paper are: econ
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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: dg-ga
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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: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: math
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph