Weak gravitational waves and Petrov classification

It is considered the problem of a superposition of the Weyl matrices with different canonical bases as sum these matrices with a point of view of Petrov’s algebraic classification of gravitational fields. Weyl matrices are close connected with the algebraic classification. Such superposition of the Weyl matrices has physical interpretation in superposition of weak gravitational fields and may be used for getting resulting gravitational field. An example of an investigation there is sum of two Weyl matrices for two gravitational plane waves of type by Petrov classification. In linear approximation we get a new resulting solution of the Einstien equations with traceless energy-momentum tensor which is nilpotent matrix of index three. The energy-momentum tensor of the electromagnetic high frequency radiation is the nilpotent matrix of index two. The optical expansion scalars; the optical scalars describing rotation and shear of new congruences in resulting gravitational field vanish. Thus the congruence with tangent eigenvector of energy-momentum tensor in the first approximation behaves as a laminary flow of perfect fluid similarly as free electromagnetic radiation.