Stability of Generalised Static Black Holes in Higher Dimensions∗

We discuss the stability of (charged) static black holes in higherdimensional spacetimes with and without cosmological constant by using gauge-invariant master equations of the Schrödinger 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.