Rotating Massive Stars in General Relativity
Abstract
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.
- Publication:
-
Proceedings of the Royal Society of London Series A
- Pub Date:
- January 1967
- DOI:
- 10.1098/rspa.1967.0013
- Bibcode:
- 1967RSPSA.296..189D