Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: General Relativistic Aberration Equation and Measurable Angle of Light
  Ray in Kerr--de Sitter Spacetime   As an extension of our previous paper, instead of the total deflection angle
$\alpha$, we will mainly focus on discussing the measurable angle of the light
ray $\psi$ at the position of the observer in Kerr--de Sitter spacetime which
includes the cosmological constant $\Lambda$. We will investigate the
contributions of the radial and transverse motions of the observer which are
connected with the radial velocity $v^r$ and transverse velocity $bv^{\phi}$
($b$ is the impact parameter) as well as the spin parameter $a$ of the central
object which induces the gravitomagnetic field or frame dragging and the
cosmological constant $\Lambda$. The general relativistic aberration equation
is employed to take into account the influence of the motion of the observer on
the measurable angle $\psi$. The measurable angle $\psi$ derived in this paper
can be applied to the observer placed within the curved and finite-distance
region in the spacetime. The equation of the light trajectory will be obtained
in such a way that the background is de Sitter spacetime instead of Minkowski
spacetime. If we assume that the lens object is the typical galaxy, the static
terms ${\cal O}(\Lambda bm, \Lambda ba)$ are basically comparable with the
second order deflection term ${\cal O}(m^2)$, and they are almost one order
smaller that of the Kerr deflection $-4ma/b^2$. The velocity-dependent terms
${\cal O}(\Lambda bm v^r, \Lambda bav^r)$ for radial motion and ${\cal
O}(\Lambda b^2mv^{\phi}, \Lambda b^2av^{\phi})$ for transverse motion are at
most two orders of magnitude smaller than the second order deflection ${\cal
O}(m^2)$. We also find that even when the radial and transverse velocities have
the same sign, their asymptotic behavior as $\phi$ approaches $0$ is differs,
and each diverges to the opposite infinity.

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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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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: nlin
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The categories of this paper are: chem-ph