Nonradial pulsations of stellar models in general relativity

In the Newtonian theory, a method was developed recently that enables one to solve the previously intractable problem of obtaining solutions to the eigenequations for the normal modes of rotating stellar models. In this paper, a closely related method is used to treat the even-parity nonradial modes of spherical stellar models in general relativity. In this treatment of generally nonbarotropic perturbations, the Lagrangian displacement is eliminated by solving for it in terms of a certain fluid perturbation quantity δ̃h (the enthalpy perturbation in the barotropic case) and the Regge-Wheeler metric perturbations K and ${\mathit{H}}_0$. One is then led to an explicitly fourth-order system, consisting of two second-order equations for either the pair K and δ̃h or K and ${\mathit{H}}_0$. The fourth-order system for K and ${\mathit{H}}_0$, from which all fluid perturbation variables have been eliminated, is relatively simple and provides a new way to compute quasinormal nonradial modes and to analyze the interaction of a stellar model with incident gravitational waves. The analyses provide insight into the connection between the Newtonian and relativistic theories of stellar pulsations. The relationship of the analyses to the recent work of Chandrasekhar and Ferrari is discussed.