Stability analysis of Newtonian polytropes
نویسندگان
چکیده
We analyze the stability of Newtonian polytropic static fluid spheres, described by the Lane-Emden equation. In the general case of arbitrary polytropic indices the Lane-Emden equation is a non-linear second order ordinary differential equation. By introducing a set of new variables, the Lane-Emden equation can be reduced to an autonomous system of two ordinary differential equations, which in turn may be transformed to another regular second order differential equation. We perform the study of stability by using linear stability analysis, the Jacobi stability analysis (Kosambi-Cartan-Chern theory) and the Lyapunov function method. Depending on the values of the polytropic index characterizing the fluid, these different methods yield different qualitative results on the stability of the solutions. On the other hand, these techniques offer a powerful method for constraining the physical properties of the Newtonian stars. ∗ [email protected] † [email protected]
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