  We give strong numerical evidence for the existence of an instability
afflicting six-dimensional Reissner-Nordstr\"om de Sitter (RNdS) black holes.
This instability is akin of the Konoplya-Zhidenko instability present in RNdS
black holes in seven spacetime dimensions and above. Moreover, we perform a
detailed analysis of the near-horizon limit of extremal RNdS black holes, and
find that unstable gravitational modes effectively behave as a massive scalar
field whose mass violates the AdS$_2$ Breitenl\"ohner-Freedman bound (if and
only if $d\geq 6$), thus providing a physical argument for the existence of the
instability. Finally, we show that the frequency spectrum of perturbations of
RNdS has a remarkable intricate structure with several bifurcations/mergers
that appears unique to RNdS black holes

High Energy Physics - Theory;General Relativity and Quantum Cosmology