- Gravitational Waves - A Review on the Conceptual Foundations of Gravitational Radiation

TL;DR

This review paper discusses the theoretical foundations of gravitational waves within Einstein's general relativity, covering derivations, wave equations, radiative losses, and current detection efforts, providing a comprehensive overview for researchers.

Contribution

It offers a detailed synthesis of the theoretical derivations, gravitational wave equations, and current detection technologies, highlighting recent advancements and future prospects.

Findings

Derivation of linearised Einstein equations

Analysis of gravitational wave emission from n-body systems

Overview of current interferometric detectors

Abstract

In this manuscript we review the theoretical foundations of gravitational waves in the framework of Albert Einstein's theory of general relativity. Following Einstein's early efforts we first derive the linearised Einstein field equations and work out the corresponding gravitational wave equation. Moreover we present the gravitational potentials in the far away wave zone field point approximation obtained from the relaxed Einstein field equations. We close this review by taking a closer look on the radiative losses of gravitating $n$-body systems and present some aspects of the current interferometric gravitational waves detectors. Each section posses a separate appendix-contribution where further computational details are displayed. To conclude we summarize the main results and present a brief outlook in terms of current ongoing efforts to build a spaced based gravitational wave observatory.