Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The superradiant instability regime of the spinning Kerr black hole   Spinning Kerr black holes are known to be superradiantly unstable to massive
scalar perturbations. We here prove that the instability regime of the composed
Kerr-black-hole-massive-scalar-field system is bounded from above by the
dimensionless inequality $M\mu < m \cdot \sqrt{{{2(1+\gamma)
(1-\sqrt{1-\gamma^2}) - \gamma^2} \over {4\gamma^2}}}$, where $\{\mu,m\}$ are
respectively the proper mass and azimuthal harmonic index of the scalar field
and $\gamma\equiv r_-/r_+$ is the dimensionless ratio between the horizon radii
of the black hole. It is further shown that this {\it analytically} derived
upper bound on the superradiant instability regime of the spinning Kerr black
hole agrees with recent {\it numerical} computations of the instability
resonance spectrum.

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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: math
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The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an