Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geroch group for Einstein spaces and holographic integrability   We review how Geroch's reduction method is extended from Ricci-flat to
Einstein spacetimes. The Ehlers-Geroch SL(2,R) group is still present in the
three-dimensional sigma-model that captures the dynamics, but only a subgroup
of it is solution-generating. Holography provides an alternative
three-dimensional perspective to integrability properties of Einstein's
equations in asymptotically anti-de Sitter spacetimes. These properties emerge
as conditions on the boundary data (metric and energy-momentum tensor) ensuring
that the hydrodynamic derivative expansion be resummed into an exact
four-dimensional Einstein geometry. The conditions at hand are invariant under
a set of transformations dubbed holographic U-duality group. The latter fills
the gap left by the Ehlers-Geroch group in Einstein spaces, and allows for
solution-generating maps mixing e.g. the mass and the nut charge.

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The categories of this paper are: ao-sci
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The categories of this paper are: math
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ