Light deflection in Observation: Angle differences between two null
  geodesics on the de Sitter spacetime with multi-lensing objects
  We derive angle differences between two null geodesics, propagating from
light sources to an observer, on the de Sitter spacetime with multi-lensing
objects. Assuming the lensing objects are mass monopoles on the de Sitter
background, we derive the metric tensor by solving the Einstein equation
perturbatively. On that spacetime, we solve a null geodesic parametrized by the
coordinate time. Using the null geodesics, we define the angle differences in a
coordinate invariant way. We take in the relativistic effects up to the first
order of perturbation and clarify the magnitude of approximation errors. We
find that the rest observer, who sees the isotropic cosmic space, implicitly
observes the effect of the cosmological constant on the angle differences
through the positions of the light sources. As a practical application, we
regard the massive black hole at our galactic center (Sgr A*) and the solar
system as the lensing objects, further a star and a flare around Sgr A* as the
light sources. We write the angle differences between these light sources using
their spatial coordinates. We find that deflections by Sgr A* remain in the
angle differences while deflections by the solar system cancel out up to the
first order of perturbation. The deflections by Sgr A* amounts around 10
microarcseconds, which is detectable in the near future observations.
