Dynamics of Newtonian and relativistic thin fluid shells
Abstract
We study the state space structure of both the Newtonian and relativistic equations of motion describing thin fluid shells, and identify and classify the fixed points of their dynamics. Using concepts borrowed from dynamical systems theory, we provide an alternative proof of a general condition for the existence of Newtonian shell oscillations. For the case of polytropic relativistic shells, we numerically determine the stability region of the parameter space that supports shell oscillations.
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