Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Resonances in Extreme Mass-Ratio Inspirals: Asymptotic and
  Hyperasymptotic Analysis   An expected source of gravitational waves for future detectors in space are
the inspirals of small compact objects into much more massive black holes.
These sources have the potential to provide a wealth of information about
astronomy and fundamental physics. On short timescales the orbit of the small
object is approximately geodesic. Generic geodesics for a Kerr black hole
spacetime have a complete set of integrals and can be characterized by three
frequencies of the motion. Over the course of an inspiral, a typical system
will pass through resonances where two of these frequencies become
commensurate. The effect of the resonance will be to alter significantly the
rate of inspiral for the duration of the resonance. Understanding the impact of
these resonances on gravitational wave phasing is important to detect and
exploit these signals for astrophysics and fundamental physics. Two
differential equations that might describe the passage of an inspiral through
such a resonance are investigated. These differ depending on whether it is the
phase or the frequency components of a Fourier expansion of the motion that are
taken to be continuous through the resonance. Asymptotic and hyperasymptotic
analysis are used to find the late-time analytic behavior of the solution for a
system that has passed through a resonance. Linearly growing (weak resonances)
or linearly decaying (strong resonances) solutions are found depending on the
strength of the resonance. In the weak-resonance case, frequency resonances
leave an imprint (a resonant memory) on the gravitational frequency evolution.
The transition between weak and strong resonances is characterized by a
square-root singularity, and as one approaches this transition from above, the
solutions to the frequency resonance equation bunch up into families
exponentially fast.

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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: math
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio