Analogue of Black Strings in Yang-Mills Gauge Theory

The classical Yang–Mills equations areanalyzed within the geometrical framework of aneffective gravity theory. Exact analytical solutions arederived for the cylindrically symmetric configurationsof the coupled gauge and isoscalar fields. Itturns out that there is an infinite family of solutionsparametrized by two real parameters, one of whichdetermines the asymptotic behavior of fields near the symmetry axis and in infinity, while the secondlocates the singularity. These configurations have asimple pole at a finite value of the radial coordinate,and physically they represent thickstring-like objects which possess the confinementproperties. It is demonstrated that the particles withgauge charge cannot move classically and quantummechanically out of the interior region. Such objectsare thus direct analogues of the blackstring gravitational configurations reportedrecently in the literature.     

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.     

Dirac particle in Riemann–Cartan spacetimes

Dynamics of a Dirac particle in general Riemann–Cartan spacetimes is considered. The Hermitian Dirac Hamiltonian is derived and is transformed to the Foldy–Wouthuysen representation for an arbitrary spacetime geometry. The contribution of the torsion field to the Foldy–Wouthuysen Hamiltonian is found. The new bounds on Cartan’s spacetime torsion are obtained.     

Conservation laws and stress–energy–momentum tensors for systems with background fields

This article attempts to delineate the roles played by non-dynamical background structures and Killing symmetries in the construction of stress–energy–momentum tensors generated from a diffeomorphism invariant action density. An intrinsic coordinate independent approach puts into perspective a number of spurious arguments that have historically lead to the main contenders, viz the Belinfante–Rosenfeld stress–energy–momentum tensor derived from a Noether current and the Einstein–Hilbert stress–energy–momentum tensor derived in the context of Einstein’s theory of general relativity. Emphasis is placed on the role played by non-dynamical background (phenomenological) structures that discriminate between properties of these tensors particularly in the context of electrodynamics in media. These tensors are used to construct conservation laws in the presence of Killing Lie-symmetric background fields.     

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.     

Quadratic Poincaré gauge theory of gravity: A comparison with the general relativity theory

The classical dynamics of the gravitational field in the Poincaré gauge theory is studied. The most general Lagrangian quadratic in curvature and torsion is considered. The relevant field equations and their solutions are analyzed in detail, with particular emphasis on the comparison of the Poincaré gauge models with the general relativity theory. We investigate correspondence between the spaces of exact solutions of these theories, both in the presence and absence of material sources, and with or without torsion. Some new exact solutions are obtained without the use of the double duality ansatz. The weak-field approximation is discussed, and gravitational radiation is considered.     

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.