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The gravitational deflection angle of light for an observer and source atfinite distance from a lens object has been studied by Ishihara et al. [Phys.Rev. D, 94, 084015 (2016)], based on the Gauss-Bonnet theorem with using theoptical metric. Their approach to finite-distance cases is limited within anasymptotically flat spacetime. By making several assumptions, we give aninterpretation of their definition from the observer's viewpoint: The observerassumes the direction of a hypothetical light emission at the observer positionand makes a comparison between the fiducial emission direction and thedirection along the real light ray. The angle between the two directions at theobserver location can be interpreted as the deflection angle by Ishihara et al.The present interpretation does not require the asymptotic flatness. Motivatedby this, we avoid such asymptotic regions to discuss another integral form ofthe deflection angle of light. This form makes it clear that the proposeddeflection angle can be used not only for asymptotically flat spacetimes butalso for asymptotically nonflat ones. We examine the proposed deflection anglein two models for the latter case; Kottler (Schwarzschild-de Sitter) solutionin general relativity and a spherical solution in Weyl conformal gravity.Effects of finite distance on the light deflection in Weyl conformal gravityresult in an extra term in the deflection angle, which may be marginallyobservable in a certain parameter region. On the other hand, those in Kottlerspacetime are beyond reach of the current technology.

Gravitational deflection angle of light: Definition by an observer and its application to an asymptotically nonflat spacetime