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

Journal Article · Mon Jan 15 00:00:00 EST 1979 · Astrophys. J.; (United States)

DOI:https://doi.org/10.1086/156769· OSTI ID:6326692

Ipser, J R; Semenzato, R

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 that 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. Dodging the question of completeness, this paper establishes 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.

• Research Organization: Department of Astronomy and Astrophysics, University of Chicago
• OSTI ID: 6326692
• Journal Information: Astrophys. J.; (United States), Vol. 227:2
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
STAR MODELS
DISTURBANCES
OSCILLATION MODES
STABILITY
GENERAL RELATIVITY THEORY
GRAVITATION
HYDRODYNAMICS
MATHEMATICAL MODELS
SPHERICAL CONFIGURATION
CONFIGURATION
FIELD THEORIES
FLUID MECHANICS
MECHANICS
640102* - Astrophysics & Cosmology- Stars & Quasi-Stellar
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