Evolution equations for the perturbations of slowly rotating relativistic stars

Abstract

We present a new derivation of the equations governing the oscillations of slowly rotating relativistic stars. Previous investigations have been mostly carried out in the Regge-Wheeler gauge. However, in this gauge the process of linearizing the Einstein field equations leads to perturbation equations in a form that cannot be used to perform numerical time evolutions. It is only through the tedious process of combining and rearranging the perturbation variables in a clever way that the system can be cast into a set of hyperbolic first-order equations, which is then well suited for the numerical integration. The equations remain quite lengthy, and we therefore rederive them in a different gauge. Using the ADM formalism, one immediately obtains a first-order hyperbolic evolution system, which is remarkably simple and can be integrated numerically without many further manipulations. Moreover, the symmetry between the polar and axial equations becomes directly apparent.