Selected spherical photon orbits around a deformed Kerr black hole

In this paper, we investigate so-called spherical photon orbits around a deformed Kerr black hole with an extra deformation parameter. The change in the azimuth $\mathrm{\Delta }\phi$ and the angle of dragging of nodes per revolution $\mathrm{\Delta }\mathrm{\Omega }$ of a complete latitudinal oscillated orbit is calculated analytically. Finally, representative six examples orbits are plotted out to illustrate how spherical photon orbits look like and exhibit some interesting behavior. Especially, this spherical photon orbits are absent in circular orbits and different from the Kerr case.