Abstract
I discuss the stability of black holes in static, electro-vacuum spacetimes of higher-dimension. I first provide a master equation for gravitational perturbations of black holes in higher dimensional static spacetimes, which corresponds to Regge-Wheeler-Zerilli equation in 4-dimensional case. Then i study the stability against linear gravitational perturbations by examining whether the spatial derivative part of the master equation has a positive self-adjoint extension. In this method, for example, higher-dimensional version of Schwarzschild black holes are shown to be stable. Using similar method, I also discuss some other static solutions e.g., generalised black holes, negative mass naked singularities, and the issue of possible boundary conditions at infinities or singularities.