Motion of r illustrated schematically. It has been projected onto the equatorial plane of the black hole. The radial turning points are r_tp1 and r_tp2 between which the motion is confined. Point P indicates the position for a given p. The whole integral path is not monotonous and should be divided into several sections, each with a maximum proper length, such as DA, DG, HG, HI, PI. From the definitions of I_0αr,I_1αr, and I_2αr (see text), one obtains , , , , and , etc.