On the implications of the nonexistence of unstable outgoing normal modes for the stability of spherical stellar models to nonradial perturbations in general relativity

Details On the implications of the nonexistence of unstable outgoing normal modes for the stability of spherical stellar models to nonradial perturbations in general relativity On the implications of the nonexistence of unstable outgoing normal modes for the stability of spherical stellar models to nonradial perturbations in general relativity

Jul 1975

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975apj...199..220i&link_type=abstract

Astrophysical Journal, vol. 199, July 1, 1975, pt. 1, p. 220-226.

Astronomy and Astrophysics

Astrophysics

5

Astronomical Models, Dynamic Stability, Relativity, Stellar Structure, Existence Theorems, Gas Dynamics, Ideal Fluids, Perturbation Theory, Space-Time Functions, Stellar Rotation, Vibration Mode

Scientific paper

This paper studies whether, without tackling the question of completeness of the normal modes, one can relate the question of the nonexistence of unstable normal modes having purely outgoing waves at large radii to the question of the stability of systems to perturbations involving gravitational radiation in general relativity. An affirmative conclusion is established for the case of nonradial perturbations of spherical relativistic stellar models; that is, it is shown that a model is stable to small nonradial perturbations essentially if and only if it does not possess an unstable outgoing normal mode. This result is combined with those of an earlier paper to show that a relativistic model is stable to nonradial perturbations if its density decreases outward monotonically and if it its relativistic Schwarzschild discriminant is positive.

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