Relativistic Strain and Electromagnetic Photon-Like Objects

This paper aims to relate some properties of photon-like objects, considered as spatially finite time-stable physical entities with dynamical structure, to well defined properties of the corresponding electromagnetic strains defined as Lie derivatives of the Minkowski (pseudo)metric with respect to the eigen vector fields of the Maxwell-Minkowski stress-energy-momentum tensor. First we recall the geometric sense of the concept of strain, then we introduce and discuss the notion for photon-like objects (PhLO). We compute then the strains along the eigen vectors of the stress-energy-momentum tensor $T_{\mu}^{\nu}$ and establish important correspondences with the divergence terms of $T_{\mu}^{\nu}$ and the terms determining some internal energy-momentum exchange between the two recognizable component-fields $F$ and $*F$ of a vacuum electromagnetic field. The role of appropriately defined Frobenius curvature is also discussed and emphasized. Finally, equations of motion and interesting PhLO-solutions are given.