Separation of spacetime and matter in polar oscillations of compact stars

Abstract: In polar oscillations of compact stars dynamical changes in spacetime and matter are in general coupled together. Based on the theory of stellar pulsation proposed by Allen et al. [Phys. Rev. D 58, 124012 (1998)], we establish a feasible approximation scheme to separate spacetime from matter in such oscillations. Two independent second-order ordinary differential equations are obtained, which lead to accurate determination of p-mode and w-mode quasi-normal modes of compact stars, respectively.