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Abstract:
Two methods for computing the damping of the non-radial oscillations of stars due to gravitational radiation emission are compared: (1) solving the complete linearized equations of general relativity and (2) using an approximate method based on the quadrupole formula. It is shown that the results of the fully relativistic calculation approach the results based on the quadrupole formula for sufficiently nonrelativistic stars. The accuracy of the approximation method is investigated by considering polytropic stars with a range of polytropic indices. The approximation is worse for larger polytropic indices, i.e. for greater central condensation. It is concluded that when Newtonian models are used to approximate relativistic ones, models with the same value of GM/(c-squared)R should be compared.
