Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integrability of Einstein deformations and desingularizations   We study the question of the integrability of Einstein deformations and
relate it to the question of the desingularization of Einstein metrics. Our
main application is a negative answer to the long-standing question of whether
or not every Einstein $4$-orbifold (which is an Einstein metric space in a
synthetic sense) is limit of smooth Einstein $4$-manifolds. We more precisely
show that spherical and hyperbolic $4$-orbifolds with the simplest
singularities cannot be Gromov-Hausdorff limits of smooth Einstein $4$-metrics
without relying on previous integrability assumptions. For this, we analyze the
integrability of deformations of Ricci-flat ALE metrics through variations of
Schoen's Pohozaev identity. Inspired by Taub's preserved quantity in General
Relativity, we also introduce preserved integral quantities based on the
symmetries of Einstein metrics. These quantities are obstructions to the
integrability of infinitesimal Einstein deformations "closing up" inside a
hypersurface - even with change of topology. We show that many previously
identified obstructions to the desingularization of Einstein $4$-metrics are
equivalent to these quantities on Ricci-flat cones. In particular, all of the
obstructions to desingularizations bubbling out Eguchi-Hanson metrics are
recovered. This lets us further interpret the obstructions to the
desingularization of Einstein metrics as a defect of integrability.

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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: eess