Topological arrangements in the equatorial timelike circular orbits of regular black holes

The study of topology opens a new frontier in understanding the characteristics of light rings in rotating black holes, as well as the equatorial timelike circular orbits found in non-rotating black holes. This work is devoted to exploring the configurations of circular orbits within the temporal dimension, characterized by the different topology in regular black holes, and determining the corresponding zero points. Using effective potential, we built the vector in the r - θ plane where the zeros of ϕ define location of the timelike circular orbits. This special feature allows one to relate timelike circular orbits with the topology. To each zero point of the vector it is possible to assign a winding number, which defines a topological characteristic for timelike circular orbits. Winding numbers of -1 and +1 are assigned for unstable and stable timelike circular orbits respectively.