A laser-source model of the gravitational field

We findian exact solution of the equations for the model with a laser beam as the source of the gravitational field in the relativistic theory of gravity. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 116, No. 3, pp. 474–480, September, 1998.     

On the possibility of gravitational collapse in the relativistic theory of gravity

In the example of dust matter, it is shown that a gravitational attractive force does not lead to the formation of “black holes” in the relativistic theory of gravity. It is proved that in the absence of matter, the gravitational field is also absent. Therefore, a vacuum is not a source of a gravitational field. The mechanism of energy production in the process of the accumulation of matter into massive objects is discussed.     

Determination of Space-Time Structures from Gravitational Perturbations

We study inverse problems for the Einstein equations with source fields in a general form. Under a microlocal linearization stability condition, we show that by generating small gravitational perturbations and measuring the responses near a freely falling observer, one can uniquely determine the background Lorentzian metric up to isometries in a region where the gravitational perturbations can travel to and return. We apply the result to two concrete examples when the source fields are scalar fields (i.e., Einstein–scalar field equations) and electromagnetic fields (i.e., Einstein-Maxwell equations). © 2019 Wiley Periodicals, Inc.     

A Kerr metric solution in tetrad theory of gravitation

Using an axial parallel vector field we obtain two exact solutions of a vacuum gravitational field equations. One of the exact solutions gives the Schwarzschild metric while the other gives the Kerr metric. The parallel vector field of the Kerr solution have an axial symmetry. The exact solution of the Kerr metric contains two constants of integration, one being the gravitational mass of the source and the other constant h is related to the angular momentum of the rotating source, when the spin density S_ij^μ of the gravitational source satisfies ∂_μS_ij^μ=0. The singularity of the Kerr solution is studied.     

Absence of gravitational radiation from a nonstatic spherically symmetric body in the relativistic theory of gravity

In the framework of the relativistic theory of gravity, we establish the absence of gravitational radiation from a nonstatic spherically symmetric source.     

Analytical Solution for the Deformation of a Cylinder under Tidal Gravitational Forces

Quite a few future high precision space missions for testing Special and General Relativity will use optical resonators which are used for laser frequency stabilisation. These devices are used for carrying out tests of the isotropy of light and of the universality of the gravitational redshift. As the resonator frequency not only depends on the speed of light but also on the resonator length, the quality of these measurements is very sensitive to elastic deformations of the optical resonator itself. As a consequence, a detailed knowledge about the deformations of the cavity is necessary. In this note we derive for the first time an analytical solution for the problem of an elastic, isotropic, homogeneous free–flying cylinder in space under the influence of a tidal gravitational force. A detailed derivation can be found in [4]. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The stress-energy tensor of matter as a gravitational field source

This article discusses the hypothesis that the universally conserved stress-energy tensor of matter is the source of the gravitational field. From this hypothesis, it immediately follows that space-time must be Riemannian. In contrast to the general theory of relativity, in the gravitational theory based on this hypothesis, the concept of an inertial coordinate system, acceleration relative to space, and the laws of conservation of the energy and angular momenta are retained. In the framework of this theory, the gravitational field is a physical field. The theory explains all observable facts of the solar system, predicts the existence of a large hidden mass of matter in a homogeneous and isotropic universe, and assumes that such a universe can only be “flat.” The theory changes the established idea of the collapse of large massive bodies. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 110, No. 1, pp. 5–24, January, 1997.     

Hypothesis ofP-odd contribution to the gravitational interactions and its consequences

A generalized Lagrangian of spinor particles in a gravitational field containingP-odd terms is proposed. It is used to obtain a quasirelativistic equation of spinors in the field of a gravitational source with nonvanishing intrinsic angular momentum in both an inertial frame and in a frame rotating with the source. For these cases the quasirelativistic Hamiltonian of a test body with nonzero intrinsic angular momentum is obtained in the classical limit; it is shown that the presence in the Hamiltonian ofP-odd terms leads to the appearance of forces that, depending on the orientation of the intrinsic angular momentum of the test body, are attractive or repulsive. It is noted that theC noninvariance of the theory can in principle result in an evolution of the universe in which particles predominate over antiparticles. Other macroscopic consequences whose experimental verification would yield information about the values of the constants introduced in the theory are noted.Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 91, No. 2, pp. 309–319, May, 1992.     

Gravitation and Electromagnetism as Geometrical Objects of a Riemann-Cartan Spacetime Structure

In this paper we first show that any coupled system consisting of a gravitational plus a free electromagnetic field can be described geometrically in the sense that both Maxwell equations and Einstein equation having as source term the energy-momentum of the electromagnetic field can be derived from a geometrical Lagrangian proportional to the scalar curvature R of a particular kind of Riemann-Cartan spacetime structure. In our model the gravitational and electromagnetic fields are identified as geometrical objects of the structure.We show moreover that the contorsion tensor of the particular Riemann-Cartan spacetime structure of our theory encodes the same information as the one contained in Chern-Simons term ${{\bf A} \wedge {\it d}{\bf A}}$ that is proportional to the spin density of the electromagnetic field. Next we show that by adding to the geometrical Lagrangian a term describing the interaction of a electromagnetic current with a general electromagnetic field plus the gravitational field, together with a term describing the matter carrier of the current we get Maxwell equations with source term and Einstein equation having as source term the sum of the energy-momentum tensors of the electromagnetic and matter terms. Finally modeling by dust charged matter the carrier of the electromagnetic current we get the Lorentz force equation. Moreover, we prove that our theory is gauge invariant. We also briefly discuss our reasons for the present enterprise.     

Gravitational field of a flat scalar wave in the relativistic theory of gravity

We solve the relativistic theory of gravity equations in the case where the gravitational field source is a flat scalar wave and analyze the solution obtained. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 118, No. 2, pp. 311–316, February, 1999.     

The generalized nordtvedt effect

We calculate the post-Newtonian oscillations of the lunar orbit predicted in various theories of gravity. It is shown that the principle of the metric nature of gravitational interaction can be verified up to the post-Newtonian level of accuracy by analyzing the data on laser monitoring of the Moon. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 110, No. 3, pp. 470–475, March, 1997.     

Gravitational radiation and the evolution of gravitational collapse in cylindrical symmetry

Using the Sparling form and a geometric construction adapted to spacetimes with a 2-dimensional isometry group, we analyse a quasi-local measure of gravitational energy. We then study the gravitational radiation through spacetime junctions in cylindrically symmetric models of gravitational collapse to singularities. The models result from the matching of collapsing dust fluids interiors with gravitational wave exteriors, given by the Einstein–Rosen type solutions. For a given choice of a frame adapted to the symmetry of the matching hypersurface, we are able to compute the total gravitational energy radiated during the collapse and state whether the gravitational radiation is incoming or outgoing, in each case. This also enables us to distinguish whether a gravitational collapse is being enhanced by the gravitational radiation.     

The energy—Momentum tensor as the source of the gravitational field and the effective Riemannian spacetime

It is shown in this paper that the assumption of the matter energy—momentum tensor is the source of the gravitational field leads naturally to an effective Riemannian geometry of spacetime.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 104, No. 3, pp. 538–542, September, 1995.     

A modified Green's function for the internal gravitational wave equation in a layer of a stratified medium with a constant shear flow

The construction of a modified Green's function for the internal gravitational wave (IGW) equation in a layer of a stratified medium when there are constant mean shear flows is considered and the basic properties of the corresponding eigenvalue problems and the modified eigenfunctions and eigenvalues are investigated. It is shown that each mode of the modified Green's function consists of a sum of three terms describing (1) the IGWs that propagate from the source, (2) the effects of a time varying source, localized in a certain neighbourhood of it, and (3) the effects of the displacement of the fluid (an internal discontinuity) caused by the source. The resulting expressions are analysed out for a constant and oscillating source of the generation of IGWs in which each of the terms of Green's function is represented in the form of simple quadratures.     

On verifying the universality of gravitational interaction using an optical method

Experiments with a laser gyro can verify the universality principle for the gravitational interaction of photons with respect to the components g_0ϕ with an accuracy no worse than 10⁻¹⁶. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 117, No. 3, pp. 498–503, December, 1998.     

External Gravitational Field of a Nonstatic Spherically Symmetric Body in the Inertial Frame

We show that the external gravitational field of a nonstatic spherically symmetric source described by a diagonal metric tensor can only be static in the field theory of gravity. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 145, No. 3, pp. 425–432, December, 2005.     

Renormalization equations in gravitational theory with higher derivatives

The structure of renormalization equations in gravitational theories with higher derivatives is considered. The gauge dependence of invariant divergences of the effective action is found to be nontrivial. The external source technique is used to construct a consistent Green's function renormalization. One- and two-loop divergences of the effective action are explicitly calculated for an arbitrary parametrization and gauge. These calculations fit the general structure of the obtained renormalization equations. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 121, No. 3, pp. 387–411, December, 1999.     

A particular solution of the relativistic theory of gravity obtained by the indefinite coordinate method

A particular solution of the equations of the relativistic theory of gravity describing the gravitational field of an infinitely thin source arranged along the z-axis is obtained by the indefinite coordinate method. In this field, the motion of massive particles is studied. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 112, No. 3, pp. 501–512, September, 1997.     

Complexity of the Gravitational Method for Linear Programming

In the gravitational method for linear programming, a particle is dropped from an interior point of the polyhedron and is allowed to move under the influence of a gravitational field parallel to the objective function direction. Once the particle falls onto the boundary of the polyhedron, its subsequent motion is constrained to be on the surface of the polyhedron with the particle moving along the steepest-descent feasible direction at any instant. Since an optimal vertex minimizes the gravitational potential, computing the trajectory of the particle yields an optimal solution to the linear program.Since the particle is not constrained to move along the edges of the polyhedron, as the simplex method does, the gravitational method seemed to have the promise of being theoretically more efficient than the simplex method. In this paper, we first show that, if the particle has zero diameter, then the worst-case time complexity of the gravitational method is exponential in the size of the input linear program. As a simple corollary of the preceding result, it follows that, even when the particle has a fixed nonzero diameter, the gravitational method has exponential time complexity. The complexity of the version of the gravitational method in which the particle diameter decreases as the algorithm progresses remains an open question.     

Numerical simulation of tunnel fires using preconditioned finite volume schemes

This article is concerned with the numerical simulation of flows at low Mach numbers which are subject to the gravitational force and strong heat sources. As a specific example for such flows, a fire event in a car tunnel will be considered in detail. The low Mach flow is treated with a preconditioning technique allowing the computation of unsteady flows, while the source terms for gravitation and heat are incorporated via an operator splitting. It is shown that a first order discretization in space is not able to compute the buoyancy forces properly on reasonable grids. The feasibility of the method is demonstrated on several test cases.