Hideyoshi Arakida, Masumi Kasai
We revisit the effect of cosmological constant $\Lambda$ on the light
deflection and its role in the cosmological lens equation. First, we re-examine
the motion of photon in the Schwarzschild spacetime, and explicitly describe
the trajectory of photon and deflection angle $\alpha$ up to the second-order
in $G$. Then the discussion is extended to the contribution of the cosmological
constant $\Lambda$ in the Schwarzschild-de Sitter or Kottler spacetime.
Contrary to the previous arguments, we emphasize the following points: (a) the
cosmological constant $\Lambda$ does appear in the orbital equation of light,
(b) nevertheless the bending angle of light $\alpha$ does not change its form
even if $\Lambda \neq 0$ since the contribution of $\Lambda$ is thoroughly
absorbed into the definition of the impact parameter, and (c) the effect of
$\Lambda$ is completely involved in the angular diameter distance $D_A$.
View original:
http://arxiv.org/abs/1110.6735
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