Relativistic Rotating Electromagnetic Fields

Abstract

In this work, we consider axially symmetric stationary electromagnetic fields in the framework of special relativity. These fields have an angular momentum density in the reference frame at rest with respect to the axis of symmetry; their Poynting vector form closed integral lines around the symmetry axis. In order to describe the state of motion of the electromagnetic field, two sets of observers are introduced: the inertial set, whose members are at rest with the symmetry axis; and the noninertial set, whose members are rotating around the symmetry axis. The rotating observers measure no Poynting vector, and they are considered as comoving with the electromagnetic field. Using explicit calculations in the covariant 3 + 1 splitting formalism, the velocity field of the rotating observers is determined and interpreted as that of the electromagnetic field. The considerations of the rotating observers split in two cases, for pure fields and impure fields, respectively. Moreover, in each case, each family of rotating observers splits in two subcases, due to regions where the electromagnetic field rotates with the speed of light. These regions are generalizations of the light cylinders found around magnetized neutron stars. In both cases, we give the explicit expressions for the corresponding velocity fields. Several examples of relevance in astrophysics and cosmology are presented, such as the rotating point magnetic dipoles and a superposition of a Coulomb electric field with the field of a point magnetic dipole.

Vanishing Poynting observers and electromagnetic field classification in Kerr and Kerr-Newman spacetimes

“…In this work we extend the analysis in our previous work [16], where we focused on rotating electromagnetic fields in Minkowski space times. To describe this class of electromagnetic fields, several families of observers were introduced, among which a special family of rotating observers for which the Poynting vector vanishes and as such they measure no net flux of electromagnetic energy, together with the opposite family of inertial observers at rest with the rotation axis who measure a net Poynting flux vector.…”

“…Here b µν is the four-dimensional projector, b = g − τ ⊗ τ ; it can also be used as a metric tensor in the physical 3-space orthogonal to τ . It is also used to define the three-dimensional scalar product A • B = −b µν A µ B ν , see [16]. The three-dimensional velocity v of any test particle can be written as:…”

“…which does not rotate since ω = * (θ (0) ∧ dθ (0) ) = 0. Nevertheless, it is accelerated, G = − * (θ (0) ∧ * dθ (0) ) = 0, see [16].…”

“…In this case, it becomes necessary to use two different families of rotating observers, one for each side of the light surface. The electromagnetic fields on the light surface are always of the pure null type [16].…”

“…In this paper, we use the theory of Cartan differential forms [16], the 3 + 1decomposition or the theory of arbitrary reference frames, the space-time signature (+, −, −, −) and a system of units in which c = 1 . Greek indices are taken to run from 0 to 3 and adopt the standard summation convention on repeated indices.…”