  We discuss the stability of (charged) static black holes in
higher-dimensional spacetimes with and without cosmological constant by using
gauge-invariant master equations of the Schroedinger equation type for black
hole perturbations derived by the authors recently. In particular, we show that
the stability of higher-dimensional Schwarzschild black holes can be proved
with the help of a technique called S-deformation of the master equations. We
also point out that higher-dimensional static black holes might be unstable
only against scalar-type perturbations in the neutral case and in the charged
case with spherically symmetric or flat horizons.
