  It has been expected that astronomical observations to detect the orbital
angular momenta of electromagnetic waves may give us a new insight into
astrophysics. Previous works pointed out the possibility that a rotating black
hole can produce orbital angular momenta of electromagnetic waves through
gravitational scattering, and the spin parameter of the black hole can be
measured by observing them. However, the mechanism how the orbital angular
momentum of the electromagnetic wave is generated by the gravitational
scattering has not been clarified sufficiently. In this paper, in order to
understand it from a point of view of gravitational lensing effects, we
consider an emitter which radiates a spherical wave of the real massless scalar
field and study the deformation of the scalar wave by the gravitational
scattering due to a black hole by invoking the geometrical optics
approximation. We show that the frame dragging caused by the rotating black
hole is not a necessary condition for generating the orbital angular momentum
of the scalar wave. However, its components parallel to the direction cosines
of images appear only if the black hole is rotating.
