Improvement on the metric reconstruction scheme in the Regge-Wheeler-Zerilli formalism

We study master variables in the Regge-Wheeler-Zerilli formalism. We show that a specific choice of new variables is suitable for studying perturbation theory from the viewpoint of radiation reaction calculations. With explicit definition of the improved master variables in terms of components of metric perturbations, we present the master equations, with source terms, and metric reconstruction formulas. In the scheme using these new variables, we do not need any time and radial integrations except for solving the master equation. We also show that the master variable for even parity modes which satisfies the same homogeneous equation as the odd parity case, obtained via Chandrasekhar transformation, does not have the good property in this sense.