Algebraically Special Gravitational Fields with the Cosmological Constant and Energy-Momentum Tensor of Electromagnetic Radiation

A class of rigorous solutions of the Einstein–Maxwell equations is obtained within the Newman–Penrose formalism for algebraically special gravitational fields with the cosmological constant and energy-momentum tensor of electromagnetic radiation given that the photon flux specifying electromagnetic radiation determines isotropic-geodesic congruence. Designations within the Newman–Penrose formalism and numbers of formulas in references are the same as in [1].     

Structure of space-time curvature

The structure of recurrently related operators of the curvature tensor and of its covariant derivatives for n-dimensional Riemannian spaces with arbitrary signature is examined. Applications to Einstein's theory of gravitation are given.Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 14, pp. 177–204, 1983.     

Segregation of 57Co Atomic Probes in the Cores of Grain Boundaries in d-Transition Metals

A new method, which has been developed to examine the structure and physical properties of cores of grain boundaries (GB's) (S.M. Klotsman, Sov. Phys. Uspech. 33, 55 (1990); V.N. Kaigorodov and S.M. Klotsman, Phys. Rev. B 49 (1994)), was used to study segregats localized in two discrete regions of polycrystals: cores of GB's and two-dimensional regions of the lattice adjacent to the GB's. This paper reports and discusses results of investigations of segregation of ⁵⁷Co atomic probes in cores of GB's in the d-transition metals Cr, Ta and W. The interaction of ⁵⁷Co AP's with GB's cores in metals is similar to their interaction with vacancies, because GB's cores are characterized, as vacancies in metals, by an excess volume and a negative charge. GB's are enriched with ⁵⁷Co in chromium and tungsten. The activation enthalpy of the ⁵⁷Co atomic probes segregation at GB's in Cr and W is proportional tothe local magnetic moment of ⁵⁷Co atomic probes. GB's cores are found to be depleted of ⁵⁷Co atomic probes in Ta.     

Algebraically special gravitational fields with single-parameter motion groups

The Newman—Penrose equations for the general class of algebraically special gravitational fields with both nonzero and zero cosmological constants are reduced for gravitational fields outside of the field sources. Then new classes of exact solutions of the nondegenerate Petrov II type are derived under the additional requirement that a single-parameter group of isometric motions exist. Kazan' State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 75–81, May, 1996.