Stability of multidimensional black holes: complete numerical analysis

We analyze evolution of gravitational perturbations of D-dimensional Schwarzschild, Reissner-Nordstr\"om, and Reissner-Nordstrom-de Sitter black holes. It is known that the effective potential for the scalar type of gravitational perturbations has negative gap near the event horizon. This gap, for some values of the parameters Q (charge), Lambda (cosmological constant) and D (number of space-time dimensions), cannot be removed by S-deformations. Thereby, there is no proof of (in)stability for those cases. In the present paper, by an extensive search of quasinormal modes, both in time and frequency domains, we shall show that spherically symmetric static black holes with arbitrary charge and positive (de Sitter) lambda-term are stable for D=5, 6, >...11. In addition, we give a complete numerical data for all three types (scalar, vector and tensor) of gravitational perturbations for multi-dimensional black holes with charge and Lambda-term. The influence of charge, Lambda-term and number of extra dimensions on black hole quasinormal spectrum is discussed.