Slowly Rotating Relativistic Stars: VII. Gravitational Radiation from the Quasi-Radial Modes

Abstract

When a relativistic star rotates slowly and rigidly, centrifugal forces flatten it slightly, thereby catalyzing a small admixture of quadrupolar vibration into its radial modes and a damping of the resulting quasi-radial modes. The damping rate $1/\tau$ of each quasi-radial mode divided by its frequency ${\sigma }^{(0)}$ is given by $(1/\tau )/{\sigma }^{(0)}=\beta ({\sigma }^{(0)}{)}^3{\Omega }^4{R}^8/M,$where $\Omega$, $R$ and $M$ are the angular velocity, radius and mass of the star, and $\beta$ is a dimensionless number that depends on the mode, on relativistic corrections, and on the structure of the star, and is typically of order unity for the fundamental quasi-radial mode in the nonrelativistic limit. In this paper we develop equations and an algorithm for computing the emitted waves and the resulting damping factor $\beta$. The rotation is treated to second-order in the angular velocity and the pulsation amplitudes are assumed small and linearized, but no other approximations are made.

The research reported in this paper was completed in 1972. The paper itself was completed and put on the arXiv in 2025. For explanation, see the box on page 2 following the Abstract