On group-theoretic approach to study Einstein's and Maxwell's equations

Basing on the classical problem of the representation theory of the orthogonal group about decomposition of the tensor product of representations on irreducible components the partial classification of Einstein's equations is obtained. A new class of Maxwell's equations of relativistic electrodynamics is singled out and studied. The pointwise irreducible decompositions of the energy-momentum tensor as well as the tensor of the electro-magnetic field are established and a physical interpretation of the corresponding components is given.