Exact solution to the homogeneous Maxwell equations in the field of a gravitational wave in linearized theory

TL;DR

This paper derives an exact solution to Maxwell's equations in a spacetime affected by a gravitational wave, revealing limitations of linearized approaches depending on wave frequency, with practical implications for electromagnetic experiments.

Contribution

It provides the first exact solution to Maxwell's equations in a gravitational wave background within linearized theory, highlighting frequency-dependent solution validity.

Findings

Exact solution to Maxwell equations in gravitational wave spacetime.

Solution validity depends on gravitational wave frequency.

Application to electromagnetic wave bouncing between conductors.

Abstract

We present the exact solution to the linearized Maxwell equations in space-time slightly curved by a gravitational wave. We show that in general, even dealing with a first-order theory in the strength of the gravitational field, the solution can not be written as the sum of the flat space-time one and a weak perturbation due to the external field. Such an impossibility arises when either the frequency of the gravitational wave is too low or too high with respect to the one of the electromagnetic field. We also provide an application of the solution to the case of an electromagnetic field bounced between two parallel conducting planes.