Gravitational waves without general relativity: A tutorial

TL;DR

This tutorial demonstrates how gravitational wave properties can be derived using electromagnetic analogies, producing results similar to general relativity in waveform but differing in polarization and angular distribution.

Contribution

It introduces a simplified calculation method for gravitational waves that matches observed waveforms without relying on full general relativity.

Findings

Waveforms nearly identical to LIGO-Virgo observations

Different polarization and angular distribution from GR

Method accessible to upper-level undergraduates

Abstract

This tutorial leads the reader through the details of calculating the properties of gravitational waves from orbiting binaries, such as two orbiting black holes. Using analogies with electromagnetic radiation, the tutorial presents a calculation that produces the same dependence on the masses of the orbiting objects, the orbital frequency, and the mass separation as does the linear version of General Relativity (GR). However, the calculation yields polarization, angular distributions, and overall power results that differ from those of GR. Nevertheless, the calculation produces waveforms that are nearly identical to the pre-binary-merger portions of the signals observed by the Laser Interferometer Gravitational-Wave Observatory (LIGO-Virgo) collaboration. The tutorial should be easily understandable by students who have taken a standard upper-level undergraduate course in electromagnetism.