Exact Plane Gravitational Waves and Electromagnetic Fields

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.

Experimental quantum cosmology in time-dependent optical media

“…The specific case of interaction with photons has also been considered. Similarly to massive particles, photons were explicitly predicted to not be created by a gravitational wave [22] but the presence of certain boundary conditions can lead to the creation of electromagnetic waves, e.g. in the presence of a background magnetic field or plasma [23,24].…”

Thomson scattering induced by gravitational waves

“…A typical example of such background gravitational field is obviously represented by a gravitational wave. Here we only recall the papers of Cooperstock [3], Zeldovich [4], Grishchuk and Polnarev [5], Montanari and Calura [6] and references cited therein. Some of the above cited works have proved the possibility of conversion of gravitational into electromagnetic energy.…”

Gravitational waves and coherent phonon states in elastic media: 1D-analysis

“…Coupling between superconductors and gravitational waves has been studied in [8][9][10]. Also, influence of electromagnetic, gravitational and gravitoelectromagnetic waves on superconductors has been investigated in [11][12][13][14][15][16][17][18][19][20]. In recent years some Authors have considered the behaviour of Bose-Einstein condensates (BEC) in presence of weak gravitational waves, discussing possible phonon excitation inside the condensate [21,22] as an example of gravitationally induced particle creation [23].…”