CNRS, Grenoble-Alpes University
We build and test an analytical model for the electromagnetic (EM) field in a galaxy. Our motivation comes from an alternative theory of gravitation, which predicts that some “interaction energy” has to be distributed in space when there is an EM field in a gravitational field; that energy could possibly contribute to the dark matter. We consider that EM field which is the sum of the fields emitted by the stars of the galaxy. We assume that the distribution of the stars, and hence that EM field, are axially symmetric. We proved  that any totally propagating, axially symmetric, vacuum Maxwell field has the following analytical expression: The EM field is the sum of a field deriving from a vector potential, and of the EM dual of such a field. Each of the two vector potentials has only an axial component of a form outlined just below — thus the EM field derives from two “quasi-scalar potentials”. Each among those two quasi-scalar potentials is the sum, over both the frequency and the axial wavenumber, of zero-order scalar Bessel beams. We want to determine the parameters of this analytical model in order that this model describe the EM field radiated by the stars of a galaxy. To this aim, we fit, by the sum of two such quasi-scalar potentials, the numerical sum of the scalar potentials, each of which is associated with a spherical wave that any given star is assumed to emit. The quality of the fitting depends on the spatial and temporal network for which it is done. The extrapolation capacity from the spatiotemporal network used for the fitting to another spatiotemporal network is limited. The axial component of the electric field is largely dominant over the radial one on the symmetry axis, but not at a distance from it.