Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral Geometry of Nuts and Bolts   We study the spectrum of Laplace operators on a one-parameter family of
gravitational instantons of bi-axial Bianchi IX type coupled to an abelian
connection with self-dual curvature. The family of geometries includes the
Taub-NUT, Taub-bolt and Euclidean Schwarzschild geometries and interpolates
between them. The interpolating geometries have conical singularities along a
submanifold of co-dimension two, but we prove that the associated Laplace
operators have natural self-adjoint extensions and study their spectra. In
particular, we determine the essential spectrum and prove that its complement,
the discrete spectrum, is infinite. We compute these eigenvalues numerically
and compare the numerical results with an analytical approximation derived from
the asymptotic Taub-NUT form of each of the geometries in our family.

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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: physics