Relativistic stellar oscillations treated as an initial value problem

Abstract

The linearized Einstein equations for a static, spherically symmetric fluid ball and its empty surroundings are considered. It is shown that, given initial data obeying the constraints, there exists a unique solution, which describes the motion of the perturbed fluid and the gravitational waves propagating inside and outside the fluid ball. The physical junction conditions for the boundary of the ball suffice to determine the evolution inside and outside of the ball in terms of initial values. The equation of state is assumed smooth and such that the density and the speed of sound remain positive for vanishing pressure.