corresponding to both the inner and outer marginally bound orbits, see Fig. \[f2\]. For completeness, the figure includes the effective potentials defining both the inner and outer marginally stable orbits. The search for the marginally bound orbits in a concrete KdS spacetime admitting stable circular orbits must be realized in a numerical way. Clearly, in the spacetimes with $y \geq 12/15^4$, the minus-family marginally bound orbits do not exist. In the spacetimes admitting stable plus-family orbits, there is $r_{\rm mb(o)} \sim r_{\rm s}$ but $r_{\rm ms(o)} \sim 0.7 r_{\rm s}$.

![Effective potentials of equatorial radial motion of test particles in black-hole spacetime ($y=10^{-4},\ a=0.6$) allowing stable circular orbits for co-rotating particles. Marginally bound (mb) orbits are given by the solid curve corresponding to $X=X_{mb+}\doteq
2.38445$. The curve has two local maxima of the same value, $E_{mb}\doteq 0.93856$, leading to inner (mb(i)) and outer (mb(o)) marginally bound orbits. The dashed effective potential defines inner marginally stable orbit (ms(i)) by coalescing local minimum and (inner) local maximum, and corresponds to $X=X_{ms(i)+}\doteq
2.20307$ with energy $E_{ms(i)+}\doteq 0.90654$. In an analogous manner the dashed-dotted potential defines outer marginally stable orbit (ms(o)) with energy $E_{ms(o)+}\doteq 0.94451$ corresponding to $X=X_{ms(o)+}\doteq 2.90538$. (Taken from Ref. .)[]{data-label="f2"}](effpots.eps){width=".6\hsize"}

In 