ar X iv : a st ro - p h / 95 12 17 0 v 1 3 0 D ec 1 99 5 Small Radius Perturbation of the Selfgravitating Gas with Cylindrical Symmetry ∗
نویسنده
چکیده
1 Abstract Self-consistent mouvement of initial perturbation in density, velocity and grav-itation potentail on the background of the stationary cylindrical configuration of the gas with gravitation and pressure in Lagrange variables have been studied. The nonlinear partial differential equation for description radius motion has been obtained. The linearization of this equation is reduced to a Klain-Gordon equation which has an analytical solution. 2 The Model Self-consistent mouvement of initial perturbation in density, velocity and gravi-tation potentail on the background of the stationary cylindrical configuration of the gas with gravitation and pressure in Lagrange variables have been studied. In [1] it is shown that a cylindrical symmetry admits an equilibrium state of the gas with selfgravitaiting and pressure. The cylinder is supposed infinity long along the axes and all physical values are dependent on the radius of cylinder only. The equilibrium is provided by the equality of gravitational force and force of gas pressure in every point. In this article the model used in [1] is appeared as a background for a small perturbations in velocity, density, pressure and grav-itataitional potentail. In general case the perturbation may depend from two coordinats and have very complicated geometrical form. It is not possible to study two-dimensional nonlinear motion in general case. But the small deviation from the stationary state admits the principle of superposition. According to this it is possible to study radius and longitudinal motions independently
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