Gravitational bending angle of light for finite distance and the
  Gauss-Bonnet theorem
  We discuss a possible extension of calculations of the bending angle of light
in a static, spherically symmetric and asymptotically flat spacetime to a
non-asymptotically flat case. We examine a relation between the bending angle
of light and the Gauss-Bonnet theorem by using the optical metric. A
correspondence between the deflection angle of light and the surface integral
of the Gaussian curvature may allow us to take account of the finite distance
from a lens object to a light source and a receiver. Using this relation, we
propose a method for calculating the bending angle of light for such cases.
Finally, this method is applied to two examples of the non-asymptotically flat
spacetimes to suggest finite-distance corrections: Kottler (Schwarzschild-de
Sitter) solution to the Einstein equation and an exact solution in Weyl
conformal gravity.
