black holes.

However, it is crucial to understand the role of the RRCC in astrophysically most relevant, rotating Kerr backgrounds. In the Kerr–de Sitter (KdS) backgrounds, we shall consider circular equatorial motion of test particles, relevant for thin discs, and equilibrium configurations of perfect fluid, relevant for thick discs. We shall focus attention on the black-hole backgrounds, but some results related to the naked-singularity backgrounds will be mentioned because of increasing theoretical evidence on possible existence of naked singularities.[@deFel-Yun:2001:CLAQG:]

Kerr–de Sitter spacetimes {#KdS spacetimes}
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In the standard Boyer–Lindquist coordinates ($t,r,\theta, \phi$) and the geometric units ($c=G=1$), the Kerr–(anti-)de Sitter geometry is given by the line element $$\begin{aligned}
               \d s^2 =  & - & \frac{\Delta_r}{I^2 \rho^2}(\d t-a\sin^2 \theta
                \d\phi)^2
                + \frac{\Delta_{\theta}\sin^2 \theta}{I^2 \rho^2}
                \left[a\d t- \left(r^2+a^2 \right) \d\phi \right]^2 \nonumber\\
                         & + & \frac{\rho^2}{\Delta_r} \d r^2 +
                \frac{\rho^2}{\Delta_{\theta}} \d\theta^2,  
                                                               \label{e1}\end{aligned}$$ where $$\begin{aligned}
        \Delta_r & = & -\frac{1}{3}\Lambda r^2 \left(r^2+a^2 \right)
                +r^2 -2Mr + a^2,  \\                            \label{e2}
        \Delta_{\theta} & = & 1+ \frac{1}{3} \Lambda a^2 \cos^2 \theta, 
  \quad I = 1 + \frac{1}{3} \Lambda a^2, 
  \quad \rho^2 = r^2 +a^2 \cos^2 \theta.                    \label{e3}\end{aligned}$$ The parameters of the spacetime are: mass ($M$), specific angular momentum ($a$), cosmological constant ($\Lambda$). It is convenient 