\doteq 1,21202.$$ KdS black holes can exist for $a^2 < a^2_{\rm crit}$ only, while KdS naked singularities can exist for both $a^2 <
a^2_{\rm crit}$ and $a^2 > a^2_{\rm crit}$.

Separation of the KdS black-hole and naked-singularity spacetimes in the parameter space $y$–$a^2$ is shown in Fig. \[f1\]. In the black-hole spacetimes there are two black-hole horizons and the cosmological horizon, with $r_{\mathrm{h}-} < r_{\mathrm{h}+}
< r_{\mathrm{c}}$. In the naked-singularity spacetimes, there is the cosmological horizon $r_{\mathrm{c}}$ only.

![Classification of the Kerr–de Sitter spacetimes. Dashed curves separate black holes and naked singularities. Full curves divide the parametric space by properties of the stable circular orbits relevant for Keplerian accretion discs. Spacetimes with both plus-family and minus-family stable circular orbits ([**I**]{} and [**V**]{}). Spacetimes with no minus-family stable circular orbits ([**II**]{} and [**VI**]{}). Spacetimes with no stable circular orbits ([**III**]{} and [**IV**]{}). Dashed-dotted curve defines the subregion of the naked-singularity spacetimes, where the plus-family circular orbits could be stable and counter-rotating (from the point of view of the LNRF), shaded is the subregion allowing stable circular orbits with $E_{+}<0$! (Taken from Ref. .)[]{data-label="f1"}](class.eps){width=".6\hsize"}

The extreme cases, when two (or all three) horizons coalesce, were discussed in detail for the case of 