Gravitational Waves: An Introduction

TL;DR

This paper provides an accessible introduction to gravitational waves, covering their theoretical foundations, wave solutions, particle interactions, and methods for solving related equations, aimed at students with basic general relativity knowledge.

Contribution

It offers a clear, pedagogical overview of gravitational wave theory, including derivations and discussions suitable for students and newcomers to the field.

Findings

Derivation of linearized Einstein's equations

Analysis of plane wave solutions and polarization

Application of Green's functions to source problems

Abstract

In this article, I present an elementary introduction to the theory of gravitational waves. This article is meant for students who have had an exposure to general relativity, but, results from general relativity used in the main discussion have been derived and discussed in the appendices. The weak gravitational field approximation is first considered and the linearized Einstein's equations are obtained. We discuss the plane wave solutions to these equations and consider the transverse-traceless (TT) gauge. We then discuss the motion of test particles in the presence of a gravitational wave and their polarization. The method of Green's functions is applied to obtain the solutions to the linearized field equations in presence of a nonrelativistic, isolated source.