Abstract
We study the small perturbations in spherical and thin disc stellar clusters surrounding a massive black hole. Because of the black hole, stars with sufficiently low angular momentum escape from the system through the loss cone. We show that the stability properties of spherical clusters crucially depend on whether the distribution of stars is monotonic or non-monotonic in angular momentum. It turns out that only non-monotonic distributions can be unstable. At the same time, instability in disc clusters is possible for both types of distribution.
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