Gravitational radiation from even-parity perturbations of stellar collapse: Mathematical formalism and numerical methods

In this paper we develop the mathematical formalism needed to study even-parity perturbations of spherical stellar collapse models, with the goal of calculating the gravitational radiation emitted during a stellar collapse to a black hole or a type-II supernova explosion. We concentrate on developing a set of gauge-invariant perturbation quantities, both inside the star and outside in the vacuum surrounding the star, their evolution equations, and equations which match the two sets of perturbation quantities at the stellar surface. The spherical background metric is assumed to be diagonal, and the method has been applied to a May-White stellar collapse code. We also discuss the initial conditions which we choose for both the stellar background and the perturbation fields. Finally, we discuss the numerical solution of this system in a computer code, and various code tests against known results