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.     

Exact solutions and particle creation for nonconformal scalar fields in homogeneous isotropic cosmological models

We solve the problem of describing scaling factors of a homogeneous isotropic space-time such that the exact solution for the scalar field with a nonconformal coupling to curvature can be obtained from solutions for the conformally coupled field by redefining the mass and momentum. We give explicit expressions in the form of Abelian integrals for the dependence of time on the scaling factor in these cases. We obtain an exact solution for the scalar field coupled to the Gauss-Bonnet-type curvature and show that the corresponding nonconformal contributions can dominate in particle creation by the gravitational field.     

A direct method for calculating Lyapunov quantities of two-dimensional dynamical systems

We discuss cosmological models involving homogeneous and isotropic Yang-Mills (YM) fields. Such models were proposed recently as an alternative to scalar models of cosmic acceleration. There exists a unique SU(2) YM configuration (generalizable to larger gauge groups) whose energy-momentum tensor is homogeneous and isotropic in space. It is parameterized by a single scalar field with a quartic potential. In the case of the closed universe the coupled YM-doublet Higgs system admits homogeneous and isotropic configurations as well. While pure Einstein-Yang-Mills (EYM) cosmology with the standard conformally invariant YM action gives rise to the hot universe, Einstein-Yang-Mills-Higgs (EYMH) cosmology has a variety of regimes which include inflationary stages and bounces, and exhibits global cycling behavior reminiscent of the multiverse developed in time. We also discuss other mechanisms of conformal symmetry breaking such as the string-inspired Born-Infeld (BI) modification of the YM action or field-theoretical quantum corrections.     

Anisotropic Cosmology with a Dilaton Field Coupled to Ghost Dark Energy

We study a dilaton scalar field coupled to ghost dark energy in an anisotropic universe. The evolution of dark energy, which dominates the universe, can be completely described by a single dilaton scalar field. This connection allows reconstructing the kinetic energy and also the dynamics of the dilaton scalar field according to the evolution of the energy density. Using the latest observational data, we obtain bounds on the ghost dark energy models and also on generalized dark matter and dark energy. For this, we investigate how the expansion history H(z) is determined by observational quantities. We calculate the evolution of density perturbations in the linear regime for both ghost and generalized ghost dark energy and compare the results with ΛCDM models. We discuss the justification of the generalized second law of thermodynamics in a Bianchi type-I universe. The obtained model is stable for large time intervals but is unstable at small times.     

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.     

Gravitational field of a massive rotating spherical shell in RTG

We obtain a continuous solution describing the gravitational field of a massive rotating shell in the relativistic theory of gravity (RTG) in an approximation linear in expansion rate but arbitrary in the magnitude of the static gravitational field. We show that the coordinate-invariant dragging effect inside the shell may be used to define a global inertial coordinate system.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 106, No. 2, pp. 315–319, February, 1996.     

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.     

Five-Dimensional General Relativity and Kaluza–Klein Theory

In five-dimensional gravity, we consider spaces admitting a family of maximally symmetric three-dimensional subspaces. We construct five-dimensional vacuum Einstein equations and introduce the analogue of the five-dimensional mass function for these spaces. The charge conservation law for this function results in the five-dimensional analogue of the Birkhoff theorem. Hence, for the spaces under consideration, the cylindricity condition is realized dynamically. For some of the obtained metrics, the regularity condition results in the closedness of the fifth coordinate. We can then relate the period of the fifth coordinate with the value of the conserved charge. We discuss the problem of separating dynamical degrees of freedom of scalar and gravitational fields obtained when reducing the initial five-dimensional action to the four-dimensional form and the related problem of the conformal ambiguity of the four-metric gauge. The parameterization of the scalar field and the four-metric that results in a conformally invariant theory of interacting scalar and gravitational fields seems most natural.     

双标量-张量几何与标量-张量引力论变分原理

<正> §1.引言 自从1915年A.Einstein奠定了广义相对论的基础以来,曾出现过各种各样的引力理论;但似乎只有标量-张量引力理论可同广义相对论媲美.看来标量-张量理论同Einstein的广义相对论一样,是一种具有生命力的引力理论. 如所周知,Einstein的广义相对论实质上是引力现象的几何化理论,即是一种引力的度规张量理论.Einstein与Weyl的物理学之几何化思想对物理学的发展曾起过、并且将     

Blowup of the solution to the Cauchy problem with arbitrary positive energy for a system of Klein–Gordon equations in the de Sitter metric

The ?⁴ model of a scalar (complex) field in the metric of an expanding universe, namely, in the de Sitter metric is considered. The initial energy of the system can have an arbitrarily high positive value. Sufficient conditions for solution blowup in a finite time are obtained. The existence of blowup is proved by applying H.A. Levine’s modified method is used.     

Gravitational field of an expanding spherically symmetric shell in RTG. Linear velocity approximation

The appearance of nonstatic behavior of the gravitational fieldof an expanding, spherically symmetric shell is shown in RTG under the linear velocity approximation for a gravitational field of arbitrary magnitude.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 108, No. 1, pp. 79–83. July, 1996.     

Cross section for capture of a particle by a spherically symmetric body and different types of finite motion in the relativistic theory of gravitation

Conclusions It is clear that all properties of the metric (1) that can be formulated in the language of its invariants are identical when these properties are considered in general relativity and in the RTG. For example, the expressions for the cross section for capture of particles by a black hole in general relativity and a sufficiently compact body in the RTG are identical. Similarly, when we consider finite motion of particles in the RTG and in general relativity there are analogous sets of different types of motion of the particles (there is only the characteristic difference in the coordinate r characterized by the relation (6)).We note that circular orbits in the gravitational field of a spherically symmetric body were considered in the framework of the RTG in [3], and it was found that these orbits exist for r>2 and are Lyapunov stable for r>5. A relation characterizing the Thomas precession identical to the corresponding expression obtained in general relativity was also obtained in [3]. Thus, differences between general relativity and the RTG can appear only in properties that are not formulated in the language of the invariants of the metric (1). Therefore, if, for example, we consider the problem of the scattering of a particle by a spherically symmetric compact body in the framework of the RTG and general relativity, then we cannot find a difference between the theories of gravitation, since the expressions for the capture cross sections are the same.Institute of Theretical and Experimental Physics. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 85, No. 1, pp. 150–154, October, 1990.     

Impossibility of gravitational collapse

In the framework of the relativistic theory of gravity, we show that a universal mechanism for stopping the process of gravitational compression of a body with large mass with its subsequent radial expansion appears because of the gravitational field tensor. This excludes the gravitational collapse and the possibility of black hole formation.     

Gravitational waves in the relativistic theory of gravity

We demonstrate that because of the causality condition, gravitational waves have no unphysical “ghost” states in the relativistic theory of gravity with the graviton having a rest mass.     

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 <Emphasis Type="Italic">k</Emphasis>-Essence in the Relativistic Theory of Gravitation and General Relativity

We consider a model of a scalar field with a nontrivial kinetic part (k-essence) on the background of a flat homogeneous isotropic universe in the framework of the relativistic theory of gravitation and general relativity. Such a scalar field simulates the substance of an ideal fluid and serves as a model of dark energy because it leads to cosmological acceleration at later times. For finding a suitable cosmological scenario, it is more convenient to determine the dependence of the energy density of such a field on the scale factor and only then find the corresponding Lagrangian. Based on the solution of such an inverse problem, we show that in the relativistic theory of gravitation, either any scalar field of this type leads to instabilities, or the compression stage ends at an unacceptably early stage. We note that a consistent model of dark energy in the relativistic theory of gravitation can be a scalar field with a negative potential (ekpyrosis) of Steinhardt–Turok. In general relativity, the k-essence model is viable and can represent both dark energy and dark matter. We consider several specific k-essence models.     

Mechanoelectromagnetic interaction in isotropic dielectrics with regard for the local displacement of mass

On the basis of the earlier proposed model of electromagnetothermomechanics of polarizable bodies, which takes into account the process of local displacement of mass, key equations for the corresponding scalar and vector potentials are written. The generalization of the Lorentz gauge, at which the equations for calculating the scalar and vector potentials of an electromagnetic field become uncoupled, is proposed. We write a resolving system of equations for potentials in the dimensionless form and obtain a parameter of interrelation of the processes of local displacement of mass and deformation. With the use of this system, the propagation of a plane harmonic wave in an infinite isotropic medium is investigated. It is shown that the model describes the dispersion of a modified elastic wave in the high-frequency region. The obtained results agree with known data presented in the literature and obtained from relations of the gradient theory of piezoelectrics.     

Countably Periodic Gibbs Measures of the Ising Model on the Cayley Tree

We diagonalize the metric Hamiltonian and evaluate the energy spectrum of the corresponding quasiparticles for a scalar field coupled to a curvature in the case of an N-dimensional homogeneous isotropic space. The energy spectrum for the quasiparticles corresponding to the diagonal form of the canonical Hamiltonian is also evaluated. We construct a modified energy–momentum tensor with the following properties: for the conformal scalar field, it coincides with the metric energy–momentum tensor; the energies of the particles corresponding to its diagonal form are equal to the oscillator frequency; and the number of such particles created in a nonstationary metric is finite. We show that the Hamiltonian defined by the modified energy–momentum tensor can be obtained as the canonical Hamiltonian under a certain choice of variables.     

Finite difference solution of viscoelastic flows by preconditioned conjugate gradients

Attention is given to preconditioned conjugate gradients in the solution of systems of partial differential equations which arise in flows of viscoelastic liquids simulated by rheological implicit models. Finite differences discretization is used together with a generalization of the incomplete Cholesky conjugate-gradient method to include asymmetric nonsingular matrices, resulted from the discretization of the kinemetic fields and the pressure recovery problem in also considered in a two-dimensional planar flow.     

Theory of the classical gravitational field and Mach's principle

Equations for a massive gravitational field are found in the framework of the special theory of relativity on the geometrization principle. The existence of a graviton mass has fundamental significance for the construction of the theory. In accordance with this theory of gravitation, a homogeneous and isotropic universe evolves cyclically from a high density to a minimum density, etc., and can only be flat. The theory predicts the existence of an appreciable amount of dark matter in the universe. The existence of black holes in the universe is completely ruled out. The theory explains all known observational facts in the solar system.Institute of High Energy Physics. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 101, No. 1, pp. 3–27, October, 1994.