Electromagnetic potentials in curved spacetimes

Abstract

Electromagnetic potentials allow for an alternative description of the Maxwell field, the electric and magnetic components of which emerge as gradients of the vector and the scalar potentials. We provide a general relativistic analysis of these potentials, by deriving their wave equations in an arbitrary Riemannian spacetime containing a generalised imperfect fluid. Some of the driving agents in the resulting wave formulae are explicitly due to the curvature of the host spacetime. Focusing on the implications of non-Euclidean geometry, we look into the linear evolution of the vector potential in Friedmann universes with nonzero spatial curvature. Our results reveal a qualitative difference in the evolution of the potential between the closed and the open Friedmann models, solely triggered by the different spatial geometry of these spacetimes. We then consider the interaction between gravitational and electromagnetic radiation and the effects of the former upon the latter. In so doing, we apply the wave formulae of both potentials to a Minkowski background and study the Weyl–Maxwell coupling at the second perturbative level. Our solutions, which apply to low-density interstellar environments away from massive compact stars, allow for the resonant amplification of both the electromagnetic potentials by gravitational-wave distortions.

Shedding light on dark bubble cosmology

“…Consequently, curvature can act as a source for electromagnetic waves. Recall that F ab can be decomposed along the world line of an observer (see [40,41] for further details)…”

Gravitational versus Magnetohydrodynamic Waves in Curved Spacetime in the Presence of Large-Scale Magnetic Fields

“…A potential energy transfer from gravitational to the EM (and the fluid) degrees of freedom due to the resonant interaction between GWs and MHD waves in curved spacetime is an irreversible process, and not only because of the resistivity of the cosmic fluid involved (in connection, see, e.g., [55,56]). In this case, the subsequent damping of the GW has a significant side effect: the production of entropy.…”

Light propagation and atom interferometry in gravity and dilaton fields

“…Similarly, in light-pulse atom interferometers [25,26,52] matter propagates within dilaton fields and consequently such devices are susceptible [53] to both EPP violations [19-21, 23, 54] and dark matter [16][17][18]22]. However, with light pulses being an essential tool to manipulate the atoms, their modified behavior in gravity [55][56][57][58][59][60][61] and dilaton fields has to be taken into account for a consistent description of such experiments.…”