  Aims. In order to understand the anisotropic properties of local radiation
field in the curved spacetime around a rotating black hole, we investigate the
appearance of a black hole seen by an observer located near the black hole.
When the black hole is in front of a source of illumination the black hole cast
shadow in the illumination. Accordingly, the appearance of the black hole is
called the black hole shadow.
  Methods. We first analytically describe the shape of the shadow in terms of
constants of motion for a photon seen by the observer in the locally
non-rotating reference frame (LNRF). Then, we newly derive the useful equation
for the solid angle of the shadow. In a third step, we can easily plot the
apparent image of the black hole shadow. Finally, we also calculate the ratio
of the photon trapped by the hole and the escape photon to the distant region
for photons emitted near the black hole.
  Results. From the shape and the size of the black hole shadow, we can
understand the signatures of the curved spacetime; i.e., the mass and spin of
the black hole. Our equations for the solid angle of the shadow has technical
advantages in calculating the photon trapping ratio. That is, this equation is
computationally very easy, and gives extremely precise results. This is because
this equation is described by the one-parameter integration with given values
of the spin and location for the black hole considered. After this, the solid
angle can be obtained without numerical calculations of the null geodesics for
photons.
