Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Light's Bending Angle due to Black Holes: From the Photon Sphere to
  Infinity   The bending angle of light is a central quantity in the theory of
gravitational lensing. We develop an analytical perturbation framework for
calculating the bending angle of light rays lensed by a Schwarzschild black
hole. Using a perturbation parameter given in terms of the gravitational radius
of the black hole and the light ray's impact parameter, we determine an
invariant series for the strong-deflection bending angle that extends beyond
the standard logarithmic deflection term used in the literature. In the
process, we discovered an improvement to the standard logarithmic deflection
term. Our perturbation framework is also used to derive as a consistency check,
the recently found weak deflection bending angle series. We also reformulate
the latter series in terms of a more natural invariant perturbation parameter,
one that smoothly transitions between the weak and strong deflection series. We
then compare our invariant strong deflection bending-angle series with the
numerically integrated exact formal bending angle expression, and find less
than 1% discrepancy for light rays as far out as twice the critical impact
parameter. The paper concludes by showing that the strong and weak deflection
bending angle series together provide an approximation that is within 1% of the
exact bending angle value for light rays traversing anywhere between the photon
sphere and infinity.

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The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: math
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The categories of this paper are: q-alg
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The categories of this paper are: physics