# Analytic Approximations in GR and Gravitational Waves

## TL;DR

This paper reviews analytic approximation methods in general relativity, focusing on post-Newtonian, gravitational self-force, and post-Minkowskian approaches, highlighting their roles in modeling gravitational waves from compact binaries.

## Contribution

It provides an overview of recent developments and interfaces among key approximation methods used in gravitational wave analysis within general relativity.

## Key findings

- Post-Newtonian approximation effectively models early inspiral phases.
- Interfaces between PN, GSF, and PM methods enhance gravitational wave modeling.
- Recent developments improve the accuracy of gravitational wave signal predictions.

## Abstract

Analytic approximation methods in general relativity play a very important role when analyzing the gravitational wave signals recently discovered by the LIGO and Virgo detectors. In this contribution, we present the state-of-the-art and some recent developments in the famous post-Newtonian (PN) or slow-motion approximation, which has successfully computed the equations of motion and the early inspiral phase of compact binary systems. We discuss also some interesting interfaces between the PN and the gravitational self-force (GSF) approach based on black-hole perturbation theory, and between PN and the post-Minkowskian (PM) approximation, namely a non-linearity expansion valid for weak field and possibly fast-moving sources.