Self-Force in the Radiation Reaction Formula: -- Adiabatic Approximation of a Metric Perturbation and an Orbit --

We propose a new metric perturbation scheme under a possible constraint of the gauge conditions in which we obtain a physically expected prediction of the orbital evolution caused by the MiSaTaQuWa self-force. In this new scheme of a metric perturbation, an adiabatic approximation is applied to both the metric perturbation and the orbit. As a result, we are able to predict the gravitational evolution of the system in the so-called radiation reaction time scale, which is longer than the dephasing time scale. However, for gravitational wave detection by LISA, this may still be insufficient. We further consider a gauge transformation in this new metric perturbation scheme, and find a special gauge condition with which we can calculate the gravitational waveform of a time scale long enough for gravitational wave detection by LISA.