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

TL;DR

This paper introduces a new metric perturbation scheme with an adiabatic approximation to predict orbital evolution due to self-force effects, aiming to improve gravitational waveform modeling for LISA detection.

Contribution

It proposes a novel gauge condition within a metric perturbation framework that enables longer-term gravitational waveform calculations relevant for LISA.

Findings

Predicts orbital evolution caused by self-force using adiabatic approximation.

Identifies a gauge condition suitable for long-term gravitational waveform computation.

Potentially improves gravitational wave modeling for space-based detectors.

Abstract

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.