Self-gravitating fluid shells and their nonspherical oscillations in Newtonian theory

We summarize the general formalism describing surface flows in three-dimens ional space in a form which is suitable for various astrophysical applicati ons. We then apply the formalism to the analysis of nonradial perturbations of self-gravitating spherical fluid shells. Spherically symmetric gravitat ing shells (or bubbles) have been used in numerous model problems especiall y in general relativity and cosmology. A radially oscillating shell was rec ently suggested as a model for a variable cosmic object. Within Newtonian g ravity we show that self-gravitating static fluid shells are unstable with respect to linear nonradial perturbations. Only shells (bubbles) with a neg ative mass (or with a charge the repulsion of which is compensated by a ten sion) are stable.