Self-gravitating fluid shells and their non-spherical oscillations in Newtonian theory

Abstract

We summarize the general formalism describing surface flows in three-dimensional space in a form which is suitable for various astrophysical applications. We then apply the formalism to the analysis of non-radial perturbations of self-gravitating spherical fluid shells. Spherically symmetric gravitating shells (or bubbles) have been used in numerous model problems especially in general relativity and cosmology. A radially oscillating shell was recently suggested as a model for a variable cosmic object. Within Newtonian gravity we show that self-gravitating static fluid shells are unstable with respect to linear non-radial perturbations. Only shells (bubbles) with a negative mass (or with a charge the repulsion of which is compensated by a tension) are stable.

20 pages, to be published in the Astrophysical Journal, typos corrected

References in corpus (5)

• Reduced phase space formalism for spherically symmetric geometry with a massive dust shell
• Gauge Invariant Hamiltonian Formalism for Spherically Symmetric Gravitating Shells
• Oscillating shells: A model for a variable cosmic object
• Quantum Decay of Domain Walls In Cosmology I: Instanton Approach
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Cited by in corpus (5)

• Gravitational instability of expanding shells: Solution with nonlinear terms
• Newtonian and General Relativistic Models of Spherical Shells
• Newtonian and General Relativistic Models of Spherical Shells - II
• Screening of the Reissner-Nordström charge by a thin-shell of dust matter
• Poisson type conformastat spherically symmetric anisotropic fluid spacetimes