“…Secondly, COs of some special spacetime might be of great importance for astrophysics and theoretical research of gravity. For example, the inner-most (or marginally) stable COs play an important role in the accretion disk theory [7,6,8] and consequently closely related to the chaotic motion [9] and behavior of gravitational waves originated from the central source such as black hole binaries [10,11]. Study of the COs in black hole spacetimes with electric charge and/or scalar field can also be used to test properties of these black holes such as their no-hair theorem and extremality [13,12,14,15,16] and even the validity of some modified gravity [17,18,19,20].…”