On some classes of exact solutions of the einstein equations. II

Certain types of spaces are investigated in a wave coordinate system in this paper. The superposition of a monochromaticity condition, as well as certain others, permitted integrating the Einstein equations completely. The solutions found can be interpreted as wave solutions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 56–59, May, 1978.     

The relationship between stress and deformation of polymers in the linear stress state

The relation between stress, strain and strain rate is proposed as a means of describing the deformation properties of polymers. The equation describes the stress-strain curve, aftereffect, and stress relaxation in polymers. The theoretical conclusions are in good agreement with the results of creep tests on kapron (nylon-6).Mekhanika Polimerov, Vol. 1, No. 5, pp. 25–29, 1965     

Classes of accurate solutions of the Einstein-Maxwell equations

Continuing the work of [1], the self-consistent system of Einstein-Maxwell vacuum equations is integrated under the additional condition of complete variable separation in the Hamilton-Jacobl equations with an external field. Fields of type (2.1) are completely considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 13–16, April, 1982.     

Gauge fields and space-time geometry

Mappings between the SU (2) Yang-Mills gauge theory and the gauge gravity theory are discussed. The global aspects are considered in the framework of the fiber-bundle technique, and three different local constructions (depending on the existence of a fixed background metric) are described in detail. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 117, No. 2, pp. 249–262, November, 1998.     

Equivalence principle and electromagnetic field: no birefringence,no dilaton,and no axion

The coupling of the electromagnetic field to gravity is discussed. In the premetric axiomatic approach based on the experimentally well established conservation laws of electric charge and magnetic flux, the Maxwell equations are the same irrespective of the presence or absence of gravity. In this sense, one can say that the charge “substratum” and the flux “substratum” are not influenced by the gravitational field directly. However, the interrelation between these fundamental substrata, formalized as the spacetime relation H = H(F) between the 2-forms of the electromagnetic excitation H and the electromagnetic field strength F, is affected by gravity. Thus the validity of the equivalence principle for electromagnetism depends on the form of the spacetime relation. We discuss the nonlocal and local linear constitutive relations and demonstrate that the spacetime metric can be accompanied also by skewon, dilaton, and axion fields. All these premetric companions of the metric may eventually lead to a violation of the equivalence principle.