Journal
GENERAL RELATIVITY AND GRAVITATION
Volume 35, Issue 8, Pages 1435-1457Publisher
KLUWER ACADEMIC/PLENUM PUBL
DOI: 10.1023/A:1024534702166
Keywords
radial perturbations; stars; anisotropic pressure
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We investigate the stability of self-gravitating spherically symmetric anisotropic spheres under radial perturbations. We consider both the Newtonian and the full general-relativistic perturbation treatment. In the general-relativistic case, we extend the variational formalism for spheres with isotropic pressure developed by Chandrasekhar. We find that, in general, when the tangential pressure is greater than the radial pressure, the stability of the anisotropic sphere is enhanced when compared to isotropic configurations. In particular, anisotropic spheres are found to be stable for smaller values of the adiabatic index gamma.
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