Localized electromagnetic and weak gravitational fields in the source-free space

Abstract

Localized electromagnetic and weak gravitational time-harmonic fields in the source-free space are treated using expansions in plane waves. The presented solutions describe fields having a very small (about several wavelengths) and clearly defined core region with maximum intensity of field oscillations. In a given Lorentz frame L, a set of the obtained exact time-harmonic solutions of the free-space homogeneous Maxwell equations consists of three subsets (storms, whirls, and tornados), for which time average energy flux is identically zero at all points, azimuthal and spiral, respectively. In any other Lorentz frame L', they will be observed as a kind of electromagnetic missile moving without dispersing at speed V<c. The solutions that describe finite-energy evolving electromagnetic storms, whirls, tornados, and weak gravitational fields with similar properties are also presented. The properties of these fields are illustrated in graphic form.