Physics
Scientific paper
Jan 1967
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1967rspsa.296..189d&link_type=abstract
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Volume 296, Issue 1445, pp. 189-200
Physics
17
Scientific paper
Equilibrium models of uniformly rotating massive stars are investigated, using a weak field, slow rotation approximation, which is shown to be adequate for all cases of interest. The fate of radial perturbations about these equilibrium configurations is investigated using a linearized stability analysis to determine the oscillation frequency σ in a peturbation propto e1σ t. An eigenvalue equation for σ^2 is obtained which can be made self adjoint with respect to the spatial metric, and a variational principle to determine σ^2 is derived. Numerical determinations of σ^2 have been carried out for a variety of masses, radii and rotational velocities, and these results are incorporated in a simple formula that gives the dependence of σ^2 on these quantities. The condition for instability, σ^2 negative, is determined, and it is found that for large masses and maximum rotation velocity, so that when centrifugal force balances gravity at the surface, a massive star becomes unstable when its radius is 208 times the Schwarzschild radius 2GM/c^2.
Durney Bernard R.
Roxburgh Ian W.
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