Some properties of the gravitational fields of a hydrodynamical fluid and dust

Conditions are obtained on the four velocity of the particles of a medium in the gravitational fields of a hydrodynamical fluid and dust, and the nature of the motion of the medium in these fields is investigated. It is shown that the gravitational fields of a hydrodynamical fluid and dust do not admit conformal mapping onto Einstein spaces which are not conformally flat spaces (spaces of constant curvature).     

Electrodynamics in the general theory of relativity 2. Properties of asymptotically planar spaces with electromagnetic radiation

The Newman-Penrose method is used to study the asymptotic behavior of spaces with finite sources and electromagnetic and gravitational radiation. Expansions are found for the Maxwell and Weyl tensors and for the metric in inverse powers of distance from the system of sources. The total energy of the system, including the energy of the gravitational and electromagnetic fields, is defined for a particular case.Translated from Izvestiya VUZ. Fizika, No. 3, pp. 7–14, March, 1970.     

Application of the K-Orbit Method to a Solution of Thermodynamics Problems for Noncompact Lie Groups

A method of solving the main thermodynamics problem of homogeneous spaces for noncompact manifolds (on the example of the noncompact unimodular Lie groups) is suggested in the present paper. The method is based on the K-orbit formalism. A formula is derived that allows the statistical sum in noncompact spaces and the Green's function of a scalar particle in background gravitational field to be calculated. The method is illustrated by an example.     

Einstein's equations as equations of imbedding and privileged frames

It is shown that Einstein's equations for empty space in a synchronous frame are equations of imbedding of three-dimensional Riemannian spaces in four-dimensional pseudo-Riemmanian spaces with R_ik=0. Choice of the privileged synchronous frame enables one to distinguish the quantities which characterize the gravitational field from those that are due to the frame's being noninertial. In particular, it is shown that the energy of the gravitational field does not contribute to the total matter energy for island systems, which agrees with Einstein's result for a spherical universe.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 78–82, March, 1976.The author thanks N. V. Mitskevich, and also the participants of the Minvuz gravitation seminar for discussion and helpful remarks.     

Strong gravitational waves in semiclosed electromagnetic universes. Complete system of Newman-Penrose equations and radial dependence of the field variables

We consider the process of integration of a complete system of Newman-Penrose equations for electrovacuum spaces of the general theory of relativity with nonzero cosmological constant. The restrictions used for the field variables correspond to strong gravitational waves in semiclosed Universes of Bertotti-Robinson type.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 29–33, December, 1987.     

Holonomies of gauge fields in twistor space 2: Hecke algebra, diffeomorphism, and graviton amplitudes

We define a theory of gravity by constructing a gravitational holonomy operator in twistor space. The theory is a gauge theory whose Chan–Paton factor is given by a trace over elements of Poincaré algebra and Iwahori–Hecke algebra. This corresponds to a fact that, in a spinor-momenta formalism, gravitational theories are invariant under spacetime translations and diffeomorphism. The former symmetry is embedded in tangent spaces of frame fields while the latter is realized by a braid trace. We make a detailed analysis on the gravitational Chan–Paton factor and show that an S-matrix functional for graviton amplitudes can be expressed in terms of a supersymmetric version of the holonomy operator. This formulation will shed a new light on studies of quantum gravity and cosmology in four dimensions.     

Effective gravitational equations induced by quantum effects of a scalar field in the Bianchi type IX spaces

The effective gravitational equations induced by quantum effects of a scalar field in the Bianchi type IX space-time are derived in the present work. The curvature tensor components and their combinations are calculated in the Bianchi type IX spaces. To estimate a one-loop effective action, the asymptotic Schwinger-DeWitt perturbative formula with consideration of terms up to the second order is used. Quantum corrections involve the fourth-order derivative of the metric; as a consequence, the background gravitational action also includes terms up to the fourth-order derivatives of the metric. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 19–24, August, 2008.     

Letter: Note on Invariants of the Weyl Tensor

Algebraically special gravitational fields are described using algebraic and differential invariants of the Weyl tensor. A type III invariant is also given and calculated for Robinson-Trautman spaces.     

Gravitoinertial reference frames in spaces with pure radiation

A method is proposed for the construction of gravitoinertial reference frames (gravito-IRF) in spaces with pure gravitational radiation. The Penrose method of conformal inversion of spaces is used.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 19–24, April, 1977.I wish to thank V. I. Rodichev, D. D. Ivanenko, and the members of the seminar directed by them for valuable critical remarks.     

Non-Abelian Stokes theorems in the Yang-Mills and gravity theories

We discuss the interpretation of the non-Abelian Stokes theorem or the Wilson loop in the Yang-Mills theory. For the “gravitational Wilson loops,” i.e., holonomies in curved d=2, 3, 4 spaces, we then derive “ non-Abelian Stokes theorems” that are similar to our formula in the Yang-Mills theory. In particular, we derive an elegant formula for the holonomy in the case of a constant-curvature background in three dimensions and a formula for small-area loops in any number of dimensions.     

Covariant treatment of particle creation in curved space-time

We propose a particle definition in external electromagnetic and gravitational fields, using two Fock spaces (‘in-and outgoing’), with the features: i) manifest gauge covariance, ii) coincidence of the vacuum persistence amplitude with that of Schwinger's formalism, iii) asymptotically quasiclassical modes.     

Spinorial Matter in Affine Theory of Gravity and the Space Problem

The purely affine theory of gravity possesses a canonical formulation. For this and other reasons, it could be a promising candidate for quantum gravity. Motivated by these perspectives, we discuss spinorial matter coupled to gravity, where the latter is described by a connection having no a priori relation to a metric. We show that one can establish a truncated spinor formalism which, for special or approximate solutions to the gravitational equations, reduces to the standard formalism. As a consequence, one arrives at "matter-induced" Riemann–Cartan spaces solving the Weyl-Cartan space problem.     

Dynamics of a gravitational field. I

A dynamic theory of a gravitational field is constructed by analogy with electromagnetic field theory in a two-dimensional space. The main point of this paper is the determination in Einstein spaces of the analogs of inertial and quasiinertial frames of reference in twodimensional space. The possibility is discussed of interpreting the velocity field of the basis of such frames of reference as potentials of the gravitational field. This then permits a dynamic theory of the gravitational field (field equations, energy characteristics) to be constructed in Maxwellian form.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 97–103, May, 1973.In conclusion, I take this opportunity of expressing thanks to Professor V. I. Rodichev for constant attention to the work.     

Centrifugal (centripetal) and Coriolis' velocities and accelerations in $$ (\bar L_n,g) $$ -spaces

The notions of centrifugal (centripetal) and Coriolis' velocities and accelerations are introduced and considered in spaces with affine connections and metrics [ -spaces] as velocities and accelerations of flows of mass elements (particles) moving in space-time. It is shown that these types of velocities and accelerations are generated by the relative motions between the mass elements. They are closely related to the kinematic characteristics of the relative velocity and relative acceleration. The centrifugal (centripetal) velocity is found to be in connection with the Hubble law. The centrifugal (centripetal) acceleration could be interpreted as gravitational acceleration as has been done in the Einstein theory of gravitation. This fact could be used as a basis for workingout new gravitational theories in spaces with affine connections and metrics.     

On gravitational shock waves in curved spacetimes

Some years ago Dray and 't Hooft found the necessary and sufficient conditions to introduce a gravitational shock wave in a particular class of vacuum solutions to Einstein's equations. We extend this work to cover cases where non-vanishing matter fields and a cosmological constant are present. The sources of gravitational waves are massless particles moving along a null surface such as a horizon in the case of black holes. After we discuss the general case we give many explicit examples. Among them are the d-dimensional charged black hole (that includes the 4-dimensional Reissner-Nordström and the d-dimensional Schwarzschild solution as subcases), the 4-dimensional De Sitter and anti-De Sitter spaces (and the Schwarzschild-De Sitter black hole), the 3-dimensional anti-De Sitter black hole, as well as backgrounds with a covariantly constant null Killing vector. We also address the analogous problem for string-inspired gravitational solutions nd give a few examples.     

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.     

Models of G time variations in diverse dimensions

A review of different cosmological models in diverse dimensions leading to a relatively small time variation in the effective gravitational constant G is presented. Among them: the 4-dimensional (4-D) general scalar-tensor model, the multidimensional vacuum model with two curved Einstein spaces, the multidimensional model with the multicomponent anisotropic “perfect fluid”, the S-brane model with scalar fields and two form fields, etc. It is shown that there exist different possible ways of explaining relatively small time variations of the effective gravitational constant G compatible with present cosmological data (e.g. acceleration): 4-dimensional scalar-tensor theories or multidimensional cosmological models with different matter sources. The experimental bounds on ? may be satisfied either in some restricted interval or for all allowed values of the synchronous time variable.     

Geodesic curvatures in kerr space

The structure of the sources of a gravitational field in Schwarzchild and Kerr spaces is investigated using the method of geodesic curvature. The curvature is calculated in Schwarzchild space for an Isotropie and time-like congruence and in Kerr space for two Isotropie congruences. An analysis of the curvature is made.