The figure is plotted in Cartesian coordinates, with the gray outer surface representing the « sphere » on which the photon travels.
The black hole is an extreme Kerr black hole
(\(\bar{a}=\frac{a}{m}=1\)) with a trigonometric spin around a vertical axis and a « polar » orbit »
(\(i=\frac{\pi}{2}\), \(l_z=0\),
\(\frac{b_{crit}}{m}=\sqrt{\frac{c^2Q_{crit}}{m^2\varepsilon^2}}=\sqrt{11+8\sqrt{2}}\simeq 4.724\)
and \(\bar{r_c}=1+\sqrt{2}\)).
The trajectory of the photon shifts to the right with each new orbit.
It is « driven » by the spin of the black hole which is the « Lense-Thirring » effect, which can be explained by the equation \(\frac{d\varphi}{dt}=\frac{2mar_c}{r_c^4+a^2r_c^2+(a^4+a^2r_c^2)\cos^2\theta+2ma^2r_c\sin^2\theta}\)
which is the sign of \(a\).