Gravitational radiation and the stability of rotating stars

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Abstract
It has been noted that all rotating stars are unstable to the radiation of gravitational waves by non-radial stellar modes. However small the rate of stellar rotation, for each set of modes (for example the p-modes) there is always a critical azimuthal wavenumber mcrit, such that modes with m > mcrit are unstable. Using a scalar theory of gravitation we calculate the growth rate of the instability explicitly in the slow-motion regime. We find that the instability grows on astronomically interesting timescales only for neutron stars with rotational periods ≲ a few milliseconds. We indicate why general relativity is likely to yield the same conclusion. We speculate briefly on a situation in which an accreting neutron star can radiate a large fraction of the accretion luminosity as gravitational waves.

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