Electromagnetic phenomena induced by weak gravitational fields. Foundations for a possible gravitational wave detector

Abstract

In the context of the weak-field approximation to the De Rham wave-vector equation, and applying the standard Lorentz gauge to both electromagnetism and gravitation, a linearized expression for the De Rham operator is derived. The derived equation is applied to solve (1) the interaction between plane, monochromatic, and polarized electromagnetic and gravitational waves and (2) the interaction between a transverse electric (,T En) mode, propagating in a rectangular wave guide, and a gravitational wave. The second result permits us to consider the possibility of a gravitational-wave antenna based on purely electromagnetic means, because new transverse electric and magnetic modes are generated, whose characteristics depend on the gravitational wave. Evidently this detector is completely different from that based on electromagnetic gravitational resonance designed by Braguinski and Manoukine. Also, in the optic limit of the De Rham equation the known expression for the equivalent index of refraction is obtained and other laws for the amplitude and polarization are derived.

On the propagation of electromagnetic radiation in the field of a plane gravitational wave

“…This system is a set of differential equations with variable coefficients. In the approach of [13][14][15][16][17][18][19] the vector potential A µ is split into two parts:…”

“…In the following years, in the framework of the linearized theory of general relativity, much work was done to describe the propagation of electromagnetic fields in a gravitational wave background using a different approach. In fact, many authors have split the electromagnetic tensor (or the 4-vector potential) into a sum of two terms: the first one is the flat spacetime solution, while the second term describes the perturbation due to the weak gravitational field (see [13][14][15][16][17][18][19][20]). Nevertheless, as will be shown in section 2, this method changes the original physical problem.…”

Using a polarized maser to detect high-frequency relic gravitational waves

“…Since |h µν | ≪ 1, F (1) µν is also small and will be evaluated up to the first order of |h µν |. As will be seen, each component F (1) µν receives two parts of contributions: one comes from the interaction between the static magnetic field and the GWs, ∝ |h µν | B(0) , the other comes from the interaction between the maser beam and the GWs, ∝ |h µν | B(0) [38,39,15]. In our designing of the detection, the static magnetic field is chosen to be so large that B(0) / B(0) ∼ 10 −5 [19].…”

Exact Plane Gravitational Waves and Electromagnetic Fields

“…This topic is very important to conceive possible further experimental verification of general relativity and also to better understand the principles underlying the theory itself. A great deal of efforts have been aimed at solving Maxwell (or de Rham) equations to first order in the gravitational wave amplitude [1][2][3][4][5][6][7][8][9][10][11][12] or, at most, to second order under geometrical optics limit [13]. However, a general solution within the framework of the full theory of general relativity would highlight the main features of a free electromagnetic field in radiative curved space-time.…”