The equations that govern rotational and tidal perturbations of stellar oscillations

A perturbation method is used to determine linear oscillations in a uniformly rotating star, and in a uniformly and synchronously rotating component of a binary system, which is accurate to the second order in the slow angular velocity. A surface perturbation due to the distortion of the star's equilibrium configuration is treated. Emphasis is placed on parallel transport, since this part of the procedure has been omitted by Saio (1981, 1982) in his investigations of the rotational and tidal perturbations of spheroidal modes in a polytropic star and of r-modes in a uniformly rotating star. The correct equations are presently established, and it is shown that Saio's omission of the Lagrangian displacement's parallel transport does not affect his corrections to the eigenfrequencies.