Electromagnetic and Gravitational Waves: the Third Dimension

TL;DR

This paper investigates the interaction of electromagnetic and gravitational plane waves with particles, revealing that particles oscillate in both transverse and propagation directions, and examines the analogy between their effects.

Contribution

It introduces a covariant approach using the Lorentz force and geodesic deviation equations, clarifying the limited analogy between electromagnetic and gravitational wave effects.

Findings

Particles oscillate in the propagation direction in both wave types

A relativistic integral of motion applies to both electromagnetic and gravitational waves

The analogy between charged particle motion in electromagnetic and gravitational waves is limited

Abstract

Plane electromagnetic and gravitational waves interact with particles in such a way as to cause them to oscillate not only in the transverse direction but also along the direction of propagation. The electromagnetic case is usually shown by use of the Hamilton-Jacobi equation and the gravitational by a transformation to a local inertial frame. Here, the covariant Lorentz force equation and the second order equation of geodesic deviation followed by the introduction of a local inertial frame are respectively used. It is often said that there is an analogy between the motion of charged particles in the field of an electromagnetic wave and the motion of test particles in the field of a gravitational wave. This analogy is examined and found to be rather limited. It is also shown that a simple special relativistic relation leads to an integral of the motion, characteristic of plane waves, that is satisfied in both cases.