  Black hole photon spheres or light rings are closely linked to astronomical
phenomena, such as the gravitational waves and the shadow in spherically
symmetric or axi-symmetric spacetime. In Cunha and Herdeiro [Phys. Rev. Lett.
124, 181101 (2020)], a topological argument was applied for the four
dimensional stationary, axi-symmetric, asymptotically flat black hole, and the
result indicates that at least, there exists one standard light ring outside
the black hole horizon for each rotation sense. Inspired by it, in this paper,
we would like to consider a similar issue for a nonrotating, static,
spherically symmetric black hole not only with asymptotically flat behavior,
but also with AdS and dS behaviors. Following Duan's topological current
$\phi$-mapping theory, the topological current and charge for the photon
spheres are introduced. The topological current is nonzero only at the zero
point of the vector field determining the location of the photon sphere. So
each photon sphere can be assigned a topological charge. Considering the full
exterior region, we find the total topological charge always equals -1. This
result confirms that there exists at least one standard photon sphere outside
of the black hole not only in asymptotically flat spacetime, but also in
asymptotically AdS and dS spacetime. Then we apply the study to the dyonic
black holes. We observe that even when more photon spheres are included, the
total topological charge stays unchanged. Moreover, for a naked singularity, it
has a vanishing topological charge, indicating that the black hole and naked
singularity are in different topological classes. It is expected that this
novel topological argument could provide an insightful idea on the study of the
black hole photon spheres or light rings, and further cast new light on the
black hole astronomical phenomena.
