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.     

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.     

Dynamical symmetry breaking in hyperbolic 4D spacetime and in extra dimensions

We study the dynamical symmetry breaking in quark matter within two different models. First, we consider the effect of gravitational catalysis of chiral and color symmetries breaking in strong gravitational field of ultrastatic hyperbolic spacetime ℝ ⊗ H ³ in the framework of an extended Nambu-Jona-Lasinio model. Second, we discuss the dynamical fermion mass generation in the flat 4-dimensional brane situated in the 5D spacetime with one extra dimension compactified on a circle. In the model, bulk fermions interact with fermions on the brane in the presence of a constant abelian gauge field A ₅ in the bulk. The influence of the A ₅-gauge field on the symmetry breaking is considered both when this field is a background parameter and a dynamical variable.     

Theory of Dark Energy and Dark Matter

In (T. Ma and S. Wang. Gravitational field equations and theory of dark matter and dark energy, Discrete and Continuous Dynamical Systems, Ser. A, 34(2): 335-366, 2014; arXiv:1206.5078v2), a new set of gravitational field equations are derived based only on 1) the Einstein principle of general relativity, and 2) the principle of interaction dynamics, due to the the presence of dark energy and dark matter. With the field equations, we show that gravity can display both attractive and repulsive behavior, and the dark matter and dark energy are just a property of gravity caused by the nonlinear interactions of the gravitational potential $g_{μv}$and its dual field. The main objectives of this paper are two-fold. The first is to study the PID-induced cosmological model, and to show explicitly, as addressed in (T. Ma and S. Wang, Astrophysical dynamics and cosmology, Journal of Mathematical Study, 47(4): 305-378, 2014), that 1) dark matter is due to the curvature of space, and 2) dark energy corresponds to the negative pressure generated by the dual gravitational potential in the field equations, and maintains the stability of geometry and large scale structure of the Universe. Second, for the gravitational field outside of a ball of centrally symmetric matter field, there exist precisely two physical parameters dictating the two-dimensional stable manifold of asymptotically flat space-time geometry, such that, as the distance to the center of the ball of the matter field increases, gravity behaves as Newtonian gravity, then additional attraction due to the curvature of space (dark matter effect), and repulsive (dark energy effect). This also clearly demonstrates that both dark matter and dark energy are just a property of gravity.     

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.     

Newtonian limit in the stabilized Randall-Sundrum model

In the stabilized Randall-Sundrum model, we obtain and solve linearized equations of motion for gravitational and scalar fields in the case of matter on the brane. We find the Newtonian limit of an effective four-dimensional theory on branes with negative tension and explicitly isolate the radion field contribution. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 2, pp. 226–236, August, 2008.     

广义相对论之守恒定律与重力波辐射

本文证明爱因斯坦之广义相对论运动方程能演变成为物质守恒定律。虽然获得的重力场能量动量张量相等于Ｌａｎｄａｕ－Ｌｉｆｓｈｉｔｚ所得的．但演变过程之物理概念是不同的。除此之外，本文分别从物体运动方程和测地线方程着手，提供了两个寻找重力波辐射的方法。     

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.     

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.     

Massive dust ball pulsating under the action of its gravitational field

We show that if we regard the gravitational field as a physical field evolving in the Minkowski space, then a massive dust ball whose mass exceeds three solar masses, in contrast to the conclusions of general relativity, does not collapse under its own gravitation but pulsates in time in the absence of dissipation. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 2, pp. 244–251, May, 2008.     

Tensor-tensor model of gravity

The main problem with the standard gauge theory of the Poincaré group realized as a subgroup of GL(5, R) is that fields, whose physical sense is unclear, appear in connection with the non-Lorentz symmetries. Here, the Poincaré fields are treated as new Yang-Mills-type tensor fields and gravity is treated as a Higgs-Goldstone field. In this case, the effective metric tensor for matter is a hybrid of two tensor fields. In the linear approximation, the massive translation gauge field gives the Yukawa-type correction to the Newtonian potential. Also, corrections to the standard Einstein post-Newtonian formulas for light deflection and radar echo delay are obtained. A spherically symmetric solution to the equations of translation gauge fields is also found. The translation gauge field leads to the existence of a singular surface, which is impenetrable to matter and can prevent gravitational collapse of a large body, inside the Schwarzschild sphere. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 113, No. 3, pp. 448–460, December, 1997. This work was supported in part by the Georgian Government and the International Science Foundation (ISF Grant No. MXL 200).     

Linearized gravity in the Randall-Sundrum model with stabilized distance between branes

We consider linearized gravity in the Randall-Sundrum model in which the distance between branes is stabilized by introducing the scalar Goldberger-Wise field. We construct the second variation Lagrangian for fluctuations of gravitational and scalar fields over the background solution and investigate its gauge invariance. We obtain, separate, and solve the corresponding equations of motion. For physical degrees of freedom, we obtain the effective four-dimensional Lagrangian describing the massless graviton, massive gravitons, and the set of massive scalar fields. We also find masses and coupling constants of these fields to the matter on the negative-tension brane. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 149, No. 3, pp. 339–353, December, 2006.     

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.     

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.     

Schwarzschild-Type Solutions in Dilaton Gravity

In the D-dimensional dilaton gravity model, we obtain and study stationary Schwarzschild-type solutions, i.e., centrally symmetric solutions in a vacuum. They form a two-parameter family of solutions: one of the parameters is an analogue of the gravitational radius, and the second parameter characterizes the intensity of the dilaton field. If the second parameter is zero, which means that the dilaton field is constant, then the expression obtained for the metric becomes the well-known Schwarzschild solution describing a black hole. But if this parameter is nonzero, then the black hole horizon does not appear. We find the parameters of quasielliptic orbits of test particles for the obtained solutions in the weak gravitational field limit. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 145, No. 1, pp. 133–143, October, 2005.     

The generalized uncertainty principle and the entropy of the Schwarzschild-anti-de Sitter black hole with a global monopole due to spin fields

Using the corrected state density in accordance with the generalized uncertainty principle, we investigate the quantum entropy of the Schwarzschild-anti-de Sitter black hole with a global monopole arising from fields with arbitrary spin s ≤ 2. We show that the quantum entropy depends not only on the black hole characteristics but also on the spin of the field and the gravity correction factor. The existence of the energy scale of symmetry breaking decreases the total entropy. Moreover, we show that the contribution of the gravitational interactions to the entropy is very important and should not be neglected.     

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.     

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.     

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.     

Refinement of the gravitational energy definition

We analyze the error arising in the well-known “energy” method for calculating the central density of a white dwarf with maximum possible mass in the framework of the theory of tetrad energy-momentum complexes of the gravitational field. We choose the preferable complex by comparing the central density calculated using each of the three complexes under study with its value obtained by numerically integrating the Einstein equations.