Electrodynamics and spacetime geometry: Astrophysical applications

TL;DR

This paper investigates how spacetime curvature influences electromagnetic phenomena in astrophysical contexts, considering non-homogeneous and anisotropic vacuum properties, and explores implications like field decay, gravitomagnetism effects, and variable light speed.

Contribution

It introduces models of vacuum electromagnetic properties that depend on spacetime geometry, relaxing traditional assumptions of homogeneity and isotropy, and analyzes their astrophysical consequences.

Findings

Electromagnetic field decay is affected by gravitational fields.

Gravitomagnetism induces magnetic terms in Gauss's law.

Spacetime curvature can cause spatial variability in the speed of light.

Abstract

After a brief review of the foundations of (pre-metric) electromagnetism, we explore some physical consequences of electrodynamics in curved spacetime. In general, new electromagnetic couplings and related phenomena are induced by the spacetime curvature. The applications of astrophysical interest considered here correspond essentially to the following geometries: the Schwarzschild spacetime and the spacetime around a rotating spherical mass in the weak field and slow rotation regime. In the latter, we use the Parameterised Post-Newtonian (PPN) formalism. We also explore the hypothesis that the electric and magnetic properties of vacuum reflect the spacetime isometries. Therefore, the permittivity and permeability tensors should not be considered homogeneous and isotropic a priori. For spherical geometries we consider the effect of relaxing the homogeneity assumption in the constitutive relations between the fields and excitations. This affects the generalized Gauss and Maxwell-Amp\`{e}re laws where the electric permittivity and magnetic permeability in vacuum depend on the radial coordinate in accordance with the local isometries of space. For the axially symmetric geometries we relax both the assumptions of homogeneity and isotropy. We explore simple solutions and discuss the physical implications related to different phenomena such as: the decay of electromagnetic fields in the presence of gravity, magnetic terms in Gauss law due to the gravitomagnetism of the spacetime around rotating objects, a frame-dragging effect on electric fields and the possibility of a spatial (radial) variability of the velocity of light in vacuum around spherical astrophysical objects for strong gravitational fields.