Pulsations of spherically symmetric systems in general relativity

The pulsation equations for spherically symmetric black hole and soliton solutions are brought into a standard form. The formulas apply to a large class of field theoretical matter models and can easily be worked out for specific examples. The close relation to the energy principle in terms of the second variation of the Schwarzschild mass is also established. The use of the general expressions is illustrated for the Einstein-Yang-Mills and the Einstein-Skyrme system. {} 1996 The American Physical Society.