Two Families of Normal Modes in Relativistic Stars

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Abstract
Normal modes of relativistic stars are examined in order to study the system consisting of a star and gravitational waves. It is found that there are two classes of normal modes in such a radiating system. They are extremely different in the decay rates of the complex eigenfrequencies. One class is a well-known family of weakly damped modes and the other is a family of strongly damped modes, which are discovered for the first time in numerical calculations for the relativistic stellar oscillations. The weakly damped modes represent the slow decay of the stellar oscillations due to gravitational radiation. As the system becomes more relativistic, the emission rate of gravitational waves increases. As a result the decay rates of these modes increase. On the other hand, the strongly damped modes essentially represent rapid decay of the gravitational waves penetrated into the star because displacements of matter inside the star are found to be very small. The decay rates of these modes decrease as the system becomes more relativistic.

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