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

TL;DR

This paper investigates the slow evolution of metric perturbations caused by quasicircular inspirals into Schwarzschild black holes, which is crucial for accurate gravitational wave modeling of EMRIs in space-based detectors.

Contribution

It provides a detailed calculation of the slow evolution of first-order metric perturbations in Lorenz gauge for EMRIs, using gauge transformations and the method of partial annihilators.

Findings

Derived the slow evolution of metric perturbations in Lorenz gauge.

Implemented gauge transformation from Regge-Wheeler gauge solutions.

Applied the method of partial annihilators to determine master functions.

Abstract

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.