Coupled Pulsations between Polar and Axial Modes in a Slowly Rotating Relativistic Star

Abstract

Rotational coupling between l-polar mode and (l + 1)-axial mode of axially symmetric pulsations is studied. Equations governing them in a slowly rotating relativistic star show that these oscillation modes couple together in first order of the rotation, while they are separated in the non-rotating case. The effect on the characteristic frequencies is examined. In the oscillations induced by the in-coming polar gravitational wave, the axial mode is always excited, so that there is no characteristic frequency, if the out-going wave condition is imposed on the axial gravitational wave. If the out-going wave condition is imposed on both modes, the coupled system shows discrete eigenfrequencies, which are exactly the same values as in the non-rotating star, that is, the eigenfrequencies for axisymmetric perturbations are not affected by the first-order rotational effect.