Metrics of Homogeneous Spaces Admitting (3.1)-Type Complete Sets

A classification has been obtained for spaces which admit complete sets of motion integrals of the (3.1)-type and are spatially homogeneous. The metrics and Killing vectors have been found in explicit form for all types of these spaces. A classification by Bianchi is given for the spaces obtained.     

Integrability of Einstein–Weyl Equations for Spatially Homogeneous Models of Type III by Bianchi

This paper deals with nonisotropic spatially homogeneous models for a self-consistent system of Einstein–Weyl equations with a spinor field. It is shown that for spaces of type III by Bianchi the system of Einstein–Weyl equations is integrable.     

Stäckel electrovacuum spaces with isotropic complete sets. Integration of field equations for the metric generalizing a space of type (1.1)

A system of Einstein-Maxwell equations is integrated for the metric that generalizes the metric of a space with full set of type (1.1). This is necessary for carrying out the classification of the corresponding Stäckel electrovacuum spaces. An algebraic classification of the solutions obtained is carried out.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 17–20, December, 1987.     

Stekkel space of electrovacuum with isotropic complete sets of the type (1.1)

A complete classification of the Stekkel spaces of the electrovacuum, admitting one isotropic Killing vector field and two Killing tensor fields, is presented. All solutions of the Einstein-Maxwell equations found refer to the Petrov type N.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 79–83, October, 1988.In conclusion we note that all solutions presented above are of the Petrov type N.     

Spatially Homogeneous Conformally Stäckel Spaces of Type (3.1)

Russian Physics Journal - In this work, we have obtained all spatially homogeneous space-time models related to the intersection of the set of Stäckel spaces of type (2.1) and the set of...     

Conformally flat Stäckel spaces in the Brans–Dicke theory

A problem of classification of the conformally flat St?ckel spaces admitting complete separation of variables in the Hamilton–Jacobi equation is studied within the framework of the Brans–Dicke scalar-tensor gravitational theory. Solutions to the field equations of the theory are found for the conformally flat St?ckel spaces of type (1.1), and explicit forms of the metric and scalar field are presented. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 54–58, February, 2009.     

Classification of null-Stäckel electrovac metrics with cosmological constant

The complete classification of the null Stäckel electrovac spacetimes is realized. For these spacetimes it is possible to integrate the geodetic equations by the complete separation of variables in the Hamilton-Jacobi equation.     

Stäckel electrovacuum spaces of type (2.1)

Classification of Stäckel electrovacuum spaces of type (2.1) is carried out. All metrics and potentials associated with the given type of spaces are obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 54–56, February, 1989.     

Conformal transformations in scalar-tensor gravitation theories

Conformal transformations in scalar-tensor gravitation theories are investigated in the present paper. It is demonstrated that the field equations of these theories can be expressed in the Vaidya form. A scalar field equation is derived based on the compatibility condition for the field equations. The conformal factor, dilaton, and restrictions on the metric are determined for the diagonal metric of type I in the Bianchi classification. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 10–14, February, 2006.     

Isotropic Steklov-conformal metrics of plane-conformal spaces

An explicit form is found for metrics that allow integration of geodesic equations for massless particles in plane-conformal spaces by complete separation of the variables in the Hamilton-Jacobi equations. Tomsk University and Tomsk State Pedagogical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 92–96, November, 1998.