Exact plane gravitational waves and electromagnetic fields

TL;DR

This paper investigates how exact gravitational plane waves influence electromagnetic fields, providing explicit solutions and demonstrating that gravitational effects induce measurable electromagnetic phenomena, even in small regions, consistent with the equivalence principle.

Contribution

It offers explicit solutions for electromagnetic fields in gravitational wave backgrounds and shows gravitational effects cannot be eliminated locally, highlighting non-tidal electromagnetic interactions.

Findings

Gravitational waves induce measurable electromagnetic effects.

Explicit solutions for electromagnetic fields in gravitational wave backgrounds.

Gravitational effects persist locally, consistent with the equivalence principle.

Abstract

The behaviour of a "test" electromagnetic field in the background of an exact gravitational plane wave is investigated in the framework of Einstein's general relativity. We have expressed the general solution to the de Rham equations as a Fourier-like integral. In the general case we have reduced the problem to a set of ordinary differential equations and have explicitly written the solution in the case of linear polarization of the gravitational wave. We have expressed our results by means of Fermi Normal Coordinates (FNC), which define the proper reference frame of the laboratory. Moreover we have provided some "gedanken experiments", showing that an external gravitational wave induces measurable effects of non tidal nature via electromagnetic interaction. Consequently it is not possible to eliminate gravitational effects on electromagnetic field, even in an arbitrarily small spatial region around an observer freely falling in the field of a gravitational wave. This is opposite to the case of mechanical interaction involving measurements of geodesic deviation effects. This behaviour is not in contrast with the principle of equivalence, which applies to arbitrarily small region of both space and time.