  In our earlier work (PRL 103 (2009) 161101) it was shown that nonextremal
highly charged Reissner-Nordstrom-de Sitter black holes are gravitationally
unstable in D>6-dimensional space-times. Here, we find accurate threshold
values of the $\Lambda$-term at which the instability of the extremally charged
black holes starts. The larger $D$ is, the smaller is the threshold value of
$\Lambda$. We have shown that the ratio $\rho = r_{h}/r_{cos}$ (where $r_{cos}$
and $r_{h}$ are the cosmological and event horizons) is proportional to
$e^{-(D-4)/2}$ at the onset of instability for D=7,8,...11, implying that the
same law should fulfill for arbitrary D. This is numerical evidence that
extremally charged Reissner-Nordstrom-de Sitter black holes are gravitationally
unstable for D>6, while asymptotically flat extremally charged
Reissner-Nordstrom black holes are stable for all D. The instability is not
connected to the horizon instability discussed recently in the literature, and,
unlike the later one, develops also outside the event horizon, that is, it can
be seen by an external observer. In addition, for the nonextremal case through
fitting of the numerical data we obtained an approximate analytical formula
which relates values of charge and the $\Lambda$-term at the onset of
instability.
