+a^2 \right)
  + 2a^2 \right]^{-1}\nonumber\\
&\times&
\bigg\{a\left[yr\left(r^2+a^2 \right)+2
                \right]L\nonumber\\
&\pm& \left.\Delta^{1/2}_r
                \left\{r^2 L^2 +r\left[\left(1+ya^2\right)r\left(r^2+a^2
                \right)+ 2a^2 \right] \right\}^{1/2}\right\}.   \label{e23}\end{aligned}$$ In the stationary regions ($\Delta_r \geq 0$), the motion is allowed where[@Bic-Stu-Bal:1989:BULAI:] $$\label{e24}
        E \geq E_{(+)}(r;L,a,y).$$

The equatorial circular orbits can be determined by solving simultaneously the equations $R(r) = 0, dR/dr = 0$. The specific energy of the orbits is given by $$\label{e38}
        E_{\pm}(r;a,y) = \frac{1-\frac{2}{r}- \left(r^2+ a^2 \right)y
                \pm a \left(\frac{1}{r^3}- y\right)^{1/2}}
                {\left[1- \frac{3}{r}- a^2y\pm 2a \left(\frac{1}{r^3}- y
                \right)^{1/2} \right]^{1/2}},$$ while the specific angular momentum of the orbits is determined by $$L_{\pm}(r;a,y) =
                - \frac{2a +ar\left(r^2 +a^2 \right)y
                \mp r\left(r^2 +a^2\right)
                \left(\frac{1}{r^3} -y \right)^{1/2}}
                {r \left[1 -\frac{3}{r}- a^2y\pm 2a
                \left(\frac{1}{r^3} -y\right)^{1/2}
                \right]^{1/2}}.     
\label{e40}$$ The relations (\[e38\])–(\[e40\]) determine two families of the circular orbits. We call them plus-family orbits and minus-family orbits[@Stu-Sla:2004:PHYSR4:] according to the $\pm$ sign in the relations (\[e38\])–(\[e40\]). Inspecting expressions (\[e38\]) and (\[e40\]), we find two reality restrictions on the circular orbits. The first one is given by the relation $$\label{e49}
        y \leq y_{\mathrm{s}} \equiv \frac{1}{r^3},$$ which introduces the notion of the “static radius”, given by the formula $r_{\mathrm{s}} = y^{-1/3}$ independently of the rotational parameter $a$. It can be compared with formally identical result in the 