# Analyzing Gravitational Waves with General Relativity

## TL;DR

This paper reviews the theoretical methods used in gravitational wave analysis, emphasizing the role of approximation techniques like post-Newtonian methods in modeling signals for detectors such as LIGO, Virgo, and LISA.

## Contribution

It provides a comprehensive overview of analytic approximation methods in general relativity, highlighting their application in gravitational wave detection and modeling compact binary systems.

## Key findings

- Post-Newtonian approximation accurately models early inspiral phases.
- Dimensional regularization solves divergence problems in calculations.
- Finite size effects influence gravitational wave emission from neutron stars.

## Abstract

After a short review of prominent properties of gravitational waves and the newly born gravitational astronomy, we focus on theoretical aspects. Analytic approximation methods in general relativity have played a crucial role in the recent discoveries of gravitational waves. They are used to build theoretical template banks for searching and analyzing the signals in the ground-based detectors LIGO and Virgo, and, further ahead, space-based LISA-like detectors. In particular, the post-Newtonian approximation describes with high accuracy the early inspiral of compact binary systems, made of black holes or neutron stars. It mainly consists of extending the Einstein quadrupole formula by a series of relativistic corrections up to high order. The compact objects are modelled by point masses with spins. The practical calculations face difficult problems of divergences, which have been solved thanks to the dimensional regularization. In the last rotations before the merger, the finite size effects and the internal structure of neutron stars (notably the internal equation of state) affect the evolution of the orbit and the emission of gravitational waves. We describe these effects within a simple Newtonian model.