How stable are Black Holes?

Einstein's theory of general relativity gives a description of gravitating systems like stars and black holes. For simple systems such as a time-independent and rotating black hole, exact and explicit solutions to the field equations of general relativity are known. It is of great interest to investigate whether these solutions are dynamical stable, i. e., if the small changes in the initial data lead to solutions with similar properties, since it is only then, that the exact and explicitly known solutions can be said to be physically relevant.