A connection between stability and the nonexistence of unstable proper normal modes for certain classes of perturbations of gravitating systems

Details A connection between stability and the nonexistence of unstable proper normal modes for certain classes of perturbations of gravitating systems A connection between stability and the nonexistence of unstable proper normal modes for certain classes of perturbations of gravitating systems

Jan 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979apj...227..590i&link_type=abstract

Astrophysical Journal, Part 1, vol. 227, Jan. 15, 1979, p. 590-595.

Astronomy and Astrophysics

Astrophysics

5

Dynamic Stability, Gravitation Theory, Newton Theory, Perturbation Theory, Relativity, Stellar Models, Hydrodynamics, Modal Response, Spheres, Systems Stability

Scientific paper

In a previous paper, it was shown how one may avoid the question of completeness and yet establish a connection between stability and the nonexistence of so-called unstable proper normal modes for the nonradial perturbations of general-relativistic spherical stellar models. In this paper, this result is generalized to include a variety of perturbations of systems in Newtonian theory and in general relativity. The generalized result is valid for certain systems and perturbations whose normal modes are governed by a self-adjoint variational principle in which the frequency of oscillation only enters quadratically. Neglecting the question of completeness, it is shown that such a system is stable if and only if it does not possess an unstable proper normal mode. The result should be valid, for example, for axisymmetric perturbations of axisymmetric rotating fluids.

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