to introduce a dimensionless cosmological parameter $$\label{e6}
        y = \frac{1}{3} \Lambda M^2.$$ For simplicity, we put $M=1$ hereafter. Equivalently, also the coordinates $t,\ r$, the line element $\d s$, and the rotational parameter of the spacetime $a$, being expressed in units of $M$, become dimensionless. We focus our attention to the case $y>0$ corresponding to the repulsive cosmological constant; then (\[e1\]) describes a KdS spacetime.

The event horizons of the spacetime are given by the pseudosingularities of the line element (\[e1\]), determined by the condition $\Delta_r =0$. The loci of the event horizons are implicitly determined by the relation $$\label{e7}
        a^2 = a^2_{\mathrm{h}}(r;y) \equiv \frac{r^2 -2r -yr^4}{yr^2 -1}.$$ It can be shown[@Stu-Sla:2004:PHYSR4:] that a critical value of the cosmological parameter exists $$\label{e11}
        y_{\mathrm{c(KdS)}} = \frac{16}{(3+2\sqrt{3})^3} \doteq 0,05924,$$ such that for $y>y_{\mathrm{c(KdS)}}$, only naked-singularity backgrounds exist for $a^2>0$. There is another critical value $y_{\mathrm{c(SdS)}} = 1/27 \doteq 0.03704$, which is limiting the existence of SdS black holes.[@Stu-Hle:1999:PHYSR4:] In the RNdS spacetimes, the critical value is[@Stu-Hle:2002:ACTPS2:] $y_{\mathrm{c(RNdS)}} = 2/27 \doteq 0.07407$.

If $y = y_{\mathrm{c(KdS)}}$, the function $a^2_{\mathrm{h}}(r;y)$ has an inflex point corresponding to a critical value of the rotation parameter of the KdS spacetimes $$\label{e13}
        a^2_{\rm crit} = \frac{3}{16} (3+ 2\sqrt{3}) 