Can the Notion of a Homogeneous Gravitational Field be Transferred from Classical Mechanics to the Relativistic Theory of Gravity?

Bogorodskii generalized the classical mechanical concept of a homogeneous gravitational field to the case of Einstein's general relativity. We seek such a generalization to the case of the relativistic theory of gravity. The corresponding solutions in these two theories differ substantially. The solution obtained in accordance with the relativistic theory of gravity does not satisfy the causality principle in that theory. The problem of constructing a generalization of the classical notion of a homogeneous gravitational field in the framework of the relativistic theory of gravity therefore remains open.     

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.     

Derivation of differential equations on the basis of extremal theory of dimensions

We show how to derive the differential equations of dynamic processes in various systems of units on the basis of extremal theory of dimensions and find out which of these systems are preferable for obtaining new theoretic results. We also obtain an unknown equation of motion in a gravitational field and the corresponding law of mechanics defining this equation.     

New ideas regarding the geometry of space-time and gravitation

In the present survey on the basis of an analysis of the problem of the energy-momentum of the gravitational field in the general theory of relativity it is shown that this theory is unsatisfactory as a concrete realization of Einstein's idea of the connection of the geometry of space-time with matter. A new theory of gravitation is proposed which alters established ideas of space-time, makes it possible to describe all present gravitational experiments, and predicts a number of fundamental consequences.Translated from Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki, Vol. 21, pp. 3–215, 1982.     

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.     

The problem of an expanding shell in the relativistic theory of gravitation

The gravitational field of an expanding shell matched in a continuously differentiable manner at its boundaries is obtained in the linear approximation of the relativistic theory of gravitation. Analysis of the second approximation of the problem indicates that there is convergence of the employed expansion with respect to the gravitational constant.Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 91, No. 2, pp. 334–345, May, 1992.     

Is the Causality Principle Violated for Gravitational Waves?

We verify the causality principle for the relativistic theory of gravity in the linear approximation. We show that the contribution of weak gravitational waves is considerably less than the contributions of the static part of the solution and the cosmological background. Therefore, the presence of weak gravitational waves does not violate the causality principle for the relativistic theory of gravity.     

引力规范理论中的一类引力波方程

该文给出了Vierbein表述的局域Lorentz群引力规范理论中的一类引力波方程。证明了Bondi平面波方程和引力孤立波方程均被该类方程所包含,这些方程的解均为该类方程在一定条件下的特解。因而这些解是与量子场论协调一致的。     

The gravitational field of a laser beam and the Generalized Uncertainty Principle

Light carries energy and therefore is source of a gravitational field. In the paper it is proven, in particular, that a laser beam is source of non-linear gravitational waves corresponding, from a quantum point of view, to spin-1 massless particles. This fact suggests both a possible solution to the old problem on the lack of gravitational attraction between two laser beams moving parallel and a new derivation of the Generalized Uncertainty Principle.     

Basic equations for the massive gravitational field

The fundamental principles of the relativistic theory of gravitation are formulated, and equations of a gravitational field with nonzero mass are derived. The theory predicts the existence in the universe of dark matter.Physics Faculty, Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 92, No. 2, pp. 191–206, August, 1992.     

Nonsymmetrical tensor potential in the relativistic theory of gravity

We suggest a theory of nonsymmetrical tensor fields in the Minkowski space. This theory generalizes the relativistic theory of gravity with a symmetrical potential and preserves all its basic postulates. The connection of the effective space-time in which the gravitational field equations can be represented possesses torsion and nonmetricity. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 123, No. 3, pp. 521–528, June, 2000.     

Holographic instant conformal symmetry breaking by colliding conical defects

We study instant conformal symmetry breaking as a holographic effect of ultrarelativistic particles moving in the AdS₃ space–time. We give a qualitative picture of this effect based on calculating the two-point correlation functions and the entanglement entropy of the corresponding boundary theory. We show that in the geodesic approximation, because of gravitational lensing of the geodesics, the ultrarelativistic massless defect produces a zone structure for correlators with broken conformal invariance. At the same time, the holographic entanglement entropy also exhibits a transition to nonconformal behavior. Two colliding massless defects produce a more diverse zone structure for correlators and the entanglement entropy.     

Induced gravity and universe creation on the domain wall in five-dimensional space-time

We present a model with a strong fermion self-interaction and an induced gravitational interaction in five-dimensional space-time. In the strong-coupling regime, this model develops a spontaneous breaking of translational invariance, which results in localizing light particles on the (3+1)-dimensional domain wall embedded in the anti-de Sitter five-dimensional space-time. We obtain the corresponding low-energy effective action and investigate kink-type vacuum solutions in a quasiflat Riemannian metric. We discuss the physics of light particles in 3+1 dimensions and establish the fundamental relations between the induced gravitational constant and both the curvature in the five-dimensional anti-de Sitter space-time and the Newton gravitational constant of our universe. Dedicated to Yu. V. Novozhilov on his 80th birthday __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 148, No. 1, pp. 4–22, July, 2006.     

Relativistic theory of gravity and a torsion field

The fundamentals of gravity theory are stated in a Minkowski space with an effective nonzero-torsion Riemann-Cartan space-time, which is more general than the Riemannian space. The theory presented thus includes a torsion field of the Einstein-Cartan type in the general concept of the relativistic theory of gravity. Expressions for the metric and canonical energy-momentum tensors of the gravitational field and nongravitational matter in the Minkowski space are found. Noncoordinate gauge transformations are introduced under which the variation of the density of the gravitational Lagrangian is a divergence expression. Translated from Teoreticheskaya i Matematischeskaya Fizika, Vol. 118, No. 1, pp. 126–132, January, 1999.     

(Ω,A_(μv))场的引力辐射理论

本文进一步探讨作者提出的Ω场论用于包含引力辐射的测试粒子运动方程.这一理论包含严格的引力辐射方程,它是场方程的逻辑结果而无需引入额外的假定,在一般动力学问题中,这一理论应改称为(Ω,A_(μv))场论.     

New mechanism of energy release in astrophysical objects

Conclusions The above qualitative analysis of the evolution of astrophysical objects shows that in the field theory of gravitation with minimal coupling objects in the regionM/a<1/3 of values of the mean gravitational potential are stable to small perturbations of their radius with unchanged rest mass.However, the mean gravitational potential of these objects increases when they capture matter surrounding them. When the mean potential reaches the valueM/a=1/3, the object passes abruptly from an infinitely stable state to an infinitely unstable state (with respect to small perturbations of its radius). Therefore, even small perturbations in the radius of the object once the critical value of the mean gravitational potential has been reached necessarily lead to expansion of the matter, which may be accompanied by the ejection of mass of this object and the release of energy.Therefore, instead of gravitational collapse, the outcome of the instability of astrophysical objects in general relativity, in the present theory there is a new mechanism of energy release.Scientific-Research Institute of Nuclear Physics at the Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 48, No. 3, pp. 275–283, September, 1981.     

Relativistic theory of gravity and a Brans-Dicke scalar field

The natural generalization of the relativistic theory of gravity (RTG) by incorporating a Brans-Dicke scalar field is discussed. The equation for a scalar-tensor gravitational field in Minkowski space and the expression for the total energy-momentum metric tensor of a gravitational field and nongravitational matter is derived from the variational principle with a gravitational Lagrangian quadratic in the first derivatives of the scalar and tensor gravitational potentials. The two-parameter spherically symmetrical static solution for vacuum equations with a zero mass tensor graviton was obtained. This solution has a true singular Schwarzschild surface. In the case of a nonzero mass graviton, an approximate nonsingular solution for the beginning of the universe was obtained. It is noted that in the frame of the scalar-tensor generalization of RTG, a nonsingular homogeneous isotropic cosmology can be represented, not only by cyclic models, but also by models with an infinitely expanding universe and a simultaneously decreasing gravitational scalar.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 106, No. 2, pp. 325–332, February, 1996.     

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.     

Causality Principle in the Relativistic Theory of Gravity

We formulate the causality principle in the relativistic theory of gravity. This principle follows directly from the basic postulates of the theory. We find the necessary conditions that physical solutions of the gravitational field equations must satisfy.