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.     

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.     

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.     

Ultrarelativistic hadrons as cosmic membranes in TeV-gravity models

We regard an ultrarelativistic hadron moving on a brane embedded in a higher-dimensional space-time as a membrane propagating on a three-brane. For hadron sizes exceeding the compactification radius and characteristic scales of five-dimensional gravitational interaction, this membrane can be regarded as a cosmic membrane in the sense that it extends to the infinities. In the five-dimensional case, a cosmic membrane produces a topological defect similar to the defect produced by a cosmic string in the four-dimensional space-time. This representation allows calculating the effects of the influence of the hadron mass on the gravitational interaction of partons belonging to the colliding hadrons.     

Large scale nonlinear effects of fluctuations in relativistic gravitation

The first fully nonlinear mean field theory of relativistic gravitation was developed in 2004. The theory makes the striking prediction that averaging or coarse graining a gravitational field changes the apparent matter content of space-time. A review of the general theory is presented, together with applications to black hole and cosmological space-times. The results strongly suggest that at least part of the dark energy may be the net large scale effect of small scale fluctuations around a mean homogeneous isotropic cosmology.     

Number theory as the ultimate physical theory

At the Planck scale doubt is cast on the usual notion of space-time and one cannot think about elementary particles. Thus, the fundamental entities of which we consider our Universe to be composed cannot be particles, fields or strings. In this paper the numbers are considered as the fundamental entities. We discuss the construction of the corresponding physical theory. A hypothesis on the quantum fluctuations of the number field is advanced for discussion. If these fluctuations actually take place then instead of the usual quantum mechanics over the complex number field a new quantum mechanics over an arbitrary field must be developed. Moreover, it is tempting to speculate that a principle of invariance of the fundamental physical laws under a change of the number field does hold. The fluctuations of the number field could appear on the Planck length, in particular in the gravitational collapse or near the cosmological singularity. These fluctuations can lead to the appearance of domains with non-Archimedean p-adic or finite geometry. We present a short review of the p-adic mathematics necessary, in this context.     

Tunneling/WKB and anomaly methods for Rindler and de sitter space-times

We consider the WKB/tunneling method explicitly in the context of its application to the Rindler and de Sitter space-times. We also present two gravitational anomaly methods (consistent and covariant). The anomaly methods applied to the Rindler space-time do not reproduce the expected Unruh radiation, because the Rindler space-time does not have an anomaly. The consistent and the covariant anomaly methods give different results for the de Sitter space-time. In contrast to them, the WKB/tunneling method is a semiclassical calculation in which the radiation is regarded as a tunneling of quantum fields across the horizon. The tunneling method is applicable in all the indicated cases. But to recover the correct Gibbons-Hawking temperature, a previously overlooked temporal piece that contributes to the total action must be taken into account.     

Universally coupled massive gravity

We derive Einstein’s equations from a linear theory in flat space-time using free-field gauge invariance and universal coupling. The gravitational potential can be either covariant or contravariant and of almost any density weight. We adapt these results to yield universally coupled massive variants of Einstein’s equations, yielding two one-parameter families of distinct theories with spin 2 and spin 0. The Freund-Maheshwari-Schonberg theory is therefore not the unique universally coupled massive generalization of Einstein’s theory, although it is privileged in some respects. The theories we derive are a subset of those found by Ogievetsky and Polubarinov by other means. The question of positive energy, which continues to be discussed, might be addressed numerically in spherical symmetry. We briefly comment on the issue of causality with two observable metrics and the need for gauge freedom and address some criticisms by Padmanabhan of field derivations of Einstein-like equations along the way. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 2, pp. 311–336, May, 2007.     

Geodesic equations for a charged particle in the unified theory of gravitational and electromagnetic interactions

A new model of gravitational and electromagnetic interactions is constructed as a version of the classical Kaluza-Klein theory based on a five-dimensional manifold as the physical space-time. The velocity space of moving particles in the model remains four-dimensional as in the standard relativity theory. The spaces of particle velocities constitute a four-dimensional distribution over a smooth five-dimensional manifold. This distribution depends only on the electromagnetic field and is independent of the metric tensor field. We prove that the equations for the geodesics whose velocity vectors always belong to this distribution are the same as the charged particle equations of motion in the general relativity theory. The gauge transformations are interpreted in geometric terms as a particular form of coordinate transformations on the five-dimensional manifold. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 119, No. 3, pp. 517–528, June, 1999.     

On the nature of time, space and gravitation

The influence of space-time models on the nature of gravitational forces is analysed.     

Instantons and gravitation theory

Some problems related to using nonperturbative quantization methods in theories of gauge fields and gravitation are studied. The unification of interactions is considered in the context of the geometric theory of gauge fields. The notion of vacuum in the unified interaction theory and the role of instantons in the vacuum structure are considered. The relation between the definitions of instantons and the energymomentum tensor of a gauge field and also the role played by the vacuum solutions to the Einstein equations in the definition of vacuum for gauge fields are demonstrated. The Schwarzschild solution, as well as the entire class of vacuum solutions to the Einstein equations, is a gravitational instanton even though the signature of the space-time metric is hyperbolic. Gravitation, oncluding the Einstein version, is considered a special case of an interaction described by a non-Abelian gauge field. Translated from Teoreticheskaya i Matematicheskaya. Fizika. Vol. 115, No. 2, pp. 312–320, May. 1998.     

Standard model of fermions on the domain wall in five-dimensional space-time

The mechanism of generation of the Standard Model for fermions on the domain wall in five-dimensional space-time is presented. As a result of self-interaction of five-dimensional fermions and gravity induced by matter fields, in the strong coupling regime, in the model there arises a spontaneous translational symmetry breaking, which leads to localization of light particles on a 3 + 1-dimensional domain wall (“3-brane”) that is embedded into a five-dimensional anti-de Sitter space-time (AdS₅). Appropriate low-energy, effective action, classical kink-like vacuum configurations for the gravity and scalar fields are investigated. Mass spectra for light composite particles and their coupling constants interaction in ultra-low-energy, which localize on the brane, are explored. We establish estimates of characteristic scales and constants interactions of the model and also a relation between the bulk five-dimensional gravitational constant, curvature of AdS₅ space-time, and brane Newton’s constants. The induced cosmological constant on the brane exactly vanishes in all orders of the theory perturbation. We find out that scalar interaction is strongly suppressed at ultra-low-energy, and the brane fluctuations (branons) are suitable “sterile” canditates for explanation of the phenomenon of Dark Matter. Bibliography: 21 titles. Dedicated to the 100th birthday of M. P. Bronstein __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 347, 2007, pp. 5–29.     

Energy flows of gravitational waves

The problem of the energy transfer produced by weak gravitational waves on a static background is solved by using the Killing vectors without introducing the momentum-energy pseudotensor. The Lagrangian, which is of the second order in metric excitations and which determines the flow and density of the energy of gravitational waves on a static spherically symmetrical space-time background, is derived. Integration over angular variables in the action integral thus reduces the problem to a two-dimensional effective problem. Energy flows on the Schwarzschild metric background are calculated. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 120, No. 1, pp. 168–176, July, 1999.     

Time-like solutions to the Lorentz force equation in time-dependent electromagnetic and gravitational fields

We find existence and multiplicity results for time-like spatially periodic trajectories of massive particles carrying an electric charge q and subjected to time-dependent gravitational and electromagnetic fields. Such trajectories are obtained by projecting, on the base space-time, time-like geodesics with respect to a suitable Kaluza-Klein metric.     

Space-time Estimates for Parabolic Type Operator and Application to Nonlinear Parabolic Equations

In this present paper we establish space-time estimates of solutions for linear parabolic type equations based on classical multipliers theory or operator semigroup theory. According to space-time estimates we first construct suitable work space L^q(0, T; L^P), moreover we study the Cauchy problem and initial boundary value problem for semilinear parabolic equation in L^q(0, T; L^P) type space.     

Short-distance space-time structure and black holes in string theory: a short review of the present status

We briefly review the present status of string theory from the viewpoint of its implications on the short-distance space-time structure and black hole physics. Special emphases are given on two closely related issues in recent developments towards nonperturbative string theory, namely, the role of the space-time uncertainty relation as a qualitative but universal characterization of the short-distance structure of string theory and the microscopic formulation of black-hole entropies. We will also suggest that the space-time uncertainty relation can be an underlying principle for the holographic property of M theory, by showing that the space-time uncertainty relation naturally explains the UV/IR relation used in a recent derivation of the holographic bound for D3 brane by Susskind and Witten.     

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.     

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。