Comparison of electromagnetic and gravitational radiation; what we can learn about each from the other

TL;DR

This paper compares electromagnetic and gravitational fields in linearized general relativity, using mathematical analysis and visualizations to highlight similarities and differences in their properties and field structures.

Contribution

It introduces a visual comparison between electromagnetic lines of force and gravitational tendex/vortex lines, providing new insights into their analogous and distinct features.

Findings

Electromagnetic and gravitational near fields are quasistatic.

Far fields are transverse and decay as 1/r.

Intermediate fields show connecting structures.

Abstract

We compare the nature of electromagnetic fields and of gravitational fields in linearized general relativity. We carry out this comparison both mathematically and visually. In particular the "lines of force" visualizations of electromagnetism are contrasted with the recently introduced tendex/vortex eigenline technique for visualizing gravitational fields. Specific solutions, visualizations, and comparisons are given for an oscillating point quadrupole source. Among the similarities illustrated are the quasistatic nature of the near fields, the transverse 1/r nature of the far fields, and the interesting intermediate field structures connecting these two limiting forms. Among the differences illustrated are the meaning of field line motion, and of the flow of energy.