A variational principle for the even-parity perturbations of spherically symmetric star clusters in general relativity

Details A variational principle for the even-parity perturbations of spherically symmetric star clusters in general relativity A variational principle for the even-parity perturbations of spherically symmetric star clusters in general relativity

May 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979apj...229.1098i&link_type=abstract

Astrophysical Journal, Part 1, vol. 229, May 1, 1979, p. 1098-1106.

Astronomy and Astrophysics

Astrophysics

1

Perturbation Theory, Relativity, Star Clusters, Stellar Motions, Variational Principles, Eigenvectors, Gravitational Fields, Isotropism, Liouville Equations, Oscillations, Parity, Space-Time Functions, Symmetry

Scientific paper

The theory of even-parity nonspherical perturbations of collisionless isotropic spherical star clusters in general relativity is developed for l greater than or equal to 2. A variational principle for the associated normal modes of oscillation is derived. In this principle, an expression for the squared frequency of oscillation is stationary with respect to arbitary acceptable variations of the independent dynamical variables if and only if the variations are carried out around the eigenfunctions of a normal mode. The stationary value of the frequency is the corresponding eigenfrequency. The form of the variational principle guarantees the applicability of a previous theorem, which implies that a cluster is unstable if and only if it possesses a so-called unstable proper normal mode. Under a weak assumption, the form of the principle also guarantees that instabilities can possibly set in only through zero-frequency modes.

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