Slow evolution of the metric perturbation due to a quasicircular inspiral into a Schwarzschild black hole

Extreme mass-ratio inspirals (EMRIs) are one of the most highly anticipated sources of gravitational radiation novel to detection by millihertz space-based detectors. To accurately estimate the parameters of EMRIs and perform precision tests of general relativity, their models should incorporate self-force theory through second-order in the small mass ratio. Due to their extreme mass ratio, EMRIs inspiral slowly when sufficiently far from merger. As such, the slow evolution of the first-order metric perturbation contributes to the source for the second-order metric perturbation, and must be accounted for in EMRI waveform models. In this paper we calculate the slow evolution of the first-order metric perturbation in the Lorenz gauge for quasicircular orbits on a Schwarzschild background in the frequency domain. Lorenz gauge solutions to the first-order metric perturbation and its slow evolution are obtained via a gauge transformation from Regge-Wheeler gauge solutions. The slow evolution of Regge-Wheeler and Zerilli master functions, in addition to a gauge field are determined using the method of partial annihilators.