RNdS spacetimes.[@Bri-Hay:1994:CLAQG:; @Hay-Nak:1994:PHYSR4:] In the KdS spacetimes, the situation is analogical. If $r_{\mathrm{h}-}=r_{\mathrm{h}+} < 
r_{\mathrm{c}}$, the extreme black-hole case occurs, if $r_{\mathrm{h}-} <
r_{\mathrm{h}+} = r_{\mathrm{c}}$, the marginal naked-singularity case occurs, if $r_{\mathrm{h}-} = r_{\mathrm{h}+} = r_{\mathrm{c}}$, the “ultra-extreme” case occurs corresponding to a naked singularity.

Thin discs {#Thin}
==========

Basic properties of thin accretion discs are determined by equatorial circular motion of test particles because any tilted disc has to be driven to the equatorial plane of the rotating spacetimes due to the dragging of inertial frames.[@Bar-Pet:1975:ASTRJ2L:]

The motion of a test particle with rest mass $m$ is given by the geodesic equations. In a separated and integrated form, the equations were obtained by Carter.[@Car:1973:BlaHol:] For the motion restricted to the equatorial plane ($\d\theta/\d \lambda = 0$, $\theta = \pi/2$) of the KdS spacetime, the Carter equations take the following form $$\begin{aligned}
        r^2 \oder{r}{\lambda} & = & \pm R^{1/2} (r), \\
                                                                \label{e14}
        r^2 \oder{\phi}{\lambda} & = & - IP_{\theta}+
                \frac{a I P_r}{\Delta_r}, \\
                                                                \label{e15}
        r^2 \oder{t}{\lambda} & = & -a I P_{\theta} +
                \frac{(r^2 +a^2) I P_r}{\Delta_r},
                                                                \label{e16}\end{aligned}$$ where $$\begin{aligned}
     & & R(r) = P^2_r -\Delta_r \left(m^2r^2 +K \right),  \\
                                                                \label{e17}
     & & P_r = I {\cal{E}} \left(r^2 +a^2 