Propagation of transverse electromagnetic waves with gravitational perturbations in an isotropic universe

The combined behavior of gravitational and electromagnetic perturbations in the radiation-dominated plasma of an isotropic universe is considered. It is shown that transverse electromagnetic waves and vector and tensor gravitational perturbations are independent of one another. The propagation of transverse electromagnetic waves during the lepton and radiation-dominated phases is determined. It is shown that the gravitational perturbations help to excite longitudinal electromagnetic fields in the radiation-dominated plasma.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 49–54, December, 1985.     

Modelling background radiation in isotropic cosmologies

Using explicit perturbations of isotropic cosmological models which describe simple gravitational waves, an isotropic tensor having the algebraic symmetries of the Bel–Robinson tensor is derived as a model of cosmic background gravitational radiation and this is used to provide an answer to the question: in what sense can an energy–momentum–stress tensor similar to that describing the cosmic microwave background radiation (neglecting anisotropies) be associated with an isotropic background of gravitational radiation?     

Critical character of gravitational-wave modulation of electric and magnetic fields in isotropic media

The exactly integrable model of the evolution of electric and magnetic fields in an isotropic dielectric medium under the action of gravitational radiation is analyzed. It is shown that as a result of the action of the gravitational radiation field, the dynamic characteristics of an electromagnetic field as a function of the dielectric constant lose continuity in a neighborhood of the value n=1.V. I. Ul'yanov Lenin Kazan' State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 28–33, September, 1993.     

Gravitational fields with groups of motions on two-dimensional transitivity hypersurfaces in a model with matter and a magnetic field

For gravitational fields with metrics which admit of groups of motions multiply — transitive on 2-dimensional space-like invariant varieties, the exact solutions of the Einstein gravitational equations are given for the case when the sources of the gravitational field are dust-like matter and a magnetic field. A magnetic field is orientated along a direction orthogonal to transitivity hypersurface. The solutions contain arbitrary functions. In the case of transitivity hypersurface of positive curvature and in the absence of a magnetic field, the solution is reduced to the Tolman spherically symmetric solution for dust-like matter. The conditions are studied under which the solutions with a magnetic field become asymptotically isotropic and approach the flat and the open Friedmann models. The case of transitivity hypersurfaces with signature (+ –) is also considered.     

Simulation of the stresses produced in large-diameter silicon wafers during thermal annealing

The three-dimensional problem of stress and strain fields in dislocation-free silicon wafers 200 and 300 mm in diameter placed horizontally on three symmetrical supports and subjected to is gravitational forces and thermal stresses formulated and solved in the isotropic approximation. Under the action of gravitational forces, a wafer is shown to have the lowest total stress when the supports are positioned at a distance of 0.6–0.7R from the center of the wafer. The shear-stress fields are calculated for all possible slip systems. The elastic-stress field in a 300-mm wafer is found to be induced mainly by gravitational forces even at a radial temperature gradient of 10 K. At this temperature gradient, the contribution from thermal stresses in a 200-mm wafer is comparable to the contribution from gravitational forces. At radial temperature gradients lower than 5 K, the contribution from thermal stresses can also be neglected for a 200-mm wafer. The maximum shear stresses calculated indicate that one should not neglect possible dislocation generation in the zone of contact between a wafer and the supports during high-temperature annealing of 200-mm and, especially, 300-mm wafers.     

Homogeneous and isotropic solutions of a gravitational theory with scalar fields

We study the homogeneous and isotropic solutions of a gravitational theory with scalar fields. Qualitative characteristics of these solutions are analyzed and important differences with respect to the usual Einstein theory are pointed out.     

NULL GEODESIC EQUATION EQUIVALENT TO THE GEOMETRIC OPTICS EQUATION

In this paper, we proved that the null geodesic equations in general isotropic metric are rigorously equivalent to the differential equations bf light rays in a medium of flat 3-dimension.,31 space, which are the fundamental equations of geometrical optics, when the effect bf gravitational field tb light ray is taken as that of a variable "refractive index"。Our results provide the basic way to strictly describe the characteristics of some gravitational fields in terms of the Euclidean framework. It may be useful in the computation of modern astrometry and gravitational Lens effects. Finally, as a special example,the deflection of Iight by gravitational field is discussed by means of the formula of pure classical geometrical optics.     

Relativistie Cosmology With Quantum Corrections

Homogeneous isotropic, anisotropic, and inhomogeneous cosmological models are studied using Einstein's general relativity with quntum corrections in field theoretical approximation. In particular we discuss coherent scalar fields and curvature squared terms in the gravitational Lagrangian. The conformal equivalence of the field equations of fourth order to general relativity with a scalar field as source is an example of the geometrization of a matter field. The aemiclassical quantum eorrections of the scalar fields can avoid the initial cosmological singularity and they lead to an inflationary evolution stage as transient attrator. The review provides new points of view on questions like the probability of the inflationary stage and the question of mechanisms for multiple inflation.     

Cosmological application on five-dimensional teleparallel theory equivalent to general relativity

A theory of(4+1)-dimensional gravity has been developed on the basis of which equivalent to the theory of general relativity by teleparallel.The fundamental gravitational field variables are the 5-dimensional(5D) vector fields(pentad),defined globally on a manifold M,and gravity is attributed to the torsion.The Lagrangian density is quadratic in the torsion tensor.We then apply the field equations to two different homogenous and isotropic geometric structures which give the same line element,i.e.,FRW in five dimensions.The cosmological parameters are calculated and some cosmological problems are discussed.     

A unification scheme for the Einstein and Maxwell theories

A unification scheme for the Einstein and Maxwell theories is developed within a Riemann-Cartan geometry. The electromagnetic field is introduced at the level of the connection and it is, in fact, coded in the torsion. Within our framework, the unification of the massless spin-one and spin-two fields requires the inclusion of a massless spin-zero field, whose introduction may give rise to a non-constant gravitational coupling. However, for the case of dust-filled homogeneous and isotropic universe the result is essentially the same as the one supplied by general relativity.     

Spherically symmetric static inhomogeneous cosmological models

Spherically symmetric static cosmological models filled with black-body radiation are considered. The models are isotropic about a central observer but inhomogeneous. It is suggested that the energy density of the free gravitational field, which is coupled to the isotropic radiation energy density, might play an important role in generating sufficient field (vacuum) energy (when converted into thermal energy) and initiate processes like inflation. On the central world line the energy density of the free gravitational field vanishes whereas the proper pressure and density of the isotropic black-body radiation are constants. Further, it is shown that the cosmological constant is no more arbitrary but given in terms of the central pressure and density. Also, at its maximum value the energy density of the free gravitational field is proved to be equal to one third of the combined value of radiation pressure and density.     

Application of types-N and -O spaces to examples of exact solutions of the gravitational equations

Analysis of the exact solutions of the gravitational equations corresponding to the collision of two gravitational plane waves (typeN) and light-like beams (typeO) and also a Kerr-Schild wave metric with conformally flat background is used to formulate theorems that indicate the resulting type of spacetime if the initial gravitational fields belong to typesN andO. A type-D Weyl matrix always appears, which is due to the nonlinear super-position of gravitational fields, in contrast to the superposition of weak gravitational fields, when the sum of the Weyl matrices for the initial fields corresponds to dropping nonlinear terms in both the curvature tensor and the field equations.Work performed under the auspices of the Russian State Scientific-Technical Program Astronomiya.Krasnoyarsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 77–82, May, 1995.     

A new algorithm for anisotropic solutions

We establish a new algorithm that generates a new solution to the Einstein field equations, with an anisotropic matter distribution, from a seed isotropic solution. The new solution is expressed in terms of integrals of an isotropic gravitational potential; and the integration can be completed exactly for particular isotropic seed metrics. A good feature of our approach is that the anisotropic solutions necessarily have an isotropic limit. We find two examples of anisotropic solutions which generalise the isothermal sphere and the Schwarzschild interior sphere. Both examples are expressed in closed form involving elementary functions only.     

Parametrized post-post-Newtonian (PP2N) formalism for the solar system

An extension of the parametrized post-Newtonian (PPN) formalism to third order in the expansion parameterm/r is used to derive analytical expressions accurate to the same order for the motion of test particles and photons in the presence of the gravitational field of the sun represented by a static, isotropic metric. The consequences of including higher-order terms are discussed in relation to the so-called classical gravitational tests for the case of general relativity theory. Present observational or experimental data are not accurate enough to detect variations due to the inclusion of higher-order terms but a planned solar probe experiment may provide information that would make such detection possible.     

Pauli equation for a particle in metric and electromagnetic fields

A Pauli theory (Pauli equation and definition of probability current and density) for a particle in weak metric and arbitrary electromagnetic fields is treated. To formulate non-relativistic quantum mechanical problems in arbitrary electromagnetic fields and weak metrics (non-inertial systems, gravitational fields which are distant fields of arbitrary distribution of masses, gravitational waves) it is not necessary to make use of the general-relativistic Dirac equation. Close analogies to the known Pauli theory with electromagnetic fields exist. For different metric fields the corresponding Hamiltonians are given. For quantum systems (H-atoms) which are disturbed by a homogeneous gravitational field and a gravitational wave the resulting shift of energy levels and the transition probability is calculated.     

No black holes: A gravitational gauge theory possibility

The most general lowest order lagrangian that can be formed from gauge-derived vierbein invariants is constrained by the hypothesis that the speed of light as measured by conventional rods and clocks of atomic constitution is independent of direction in a gravitational field. It is shown that the standard weak field observational tests of general relativity serve to eliminate all possible combinations of parameters in this constrained lagrangian except two. One parameter choice gives the isotropic Schwarzchild black hole metric of the general theory of relativity. The other allowable choice leads to an exponential metric of the class proposed by Yilmaz, corresponding in strong fields to large red shifts without black hole formation.     

One-dimensional finite motion of a particle in the field of a weak gravitational wave

The Hamiltonian formalism of classical mechanics can be used effectively to describe the motion of a particle (including a massless one) along a segment of material that is in a nonsteady gravitational field. The problem of applying this formalism to the detection of gravitational waves using a Michelson or Fabry—Perot interferometer is considered. The existence of a phase shift of an electromagnetic wave due to the interaction of the electromagnetic and gravitational fields is noted. Moscow State Aviation Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 13–17, August, 1997.     

On Lynden-Bell and Katz's definition of gravitational field energy

The covariant definition of gravitational field energy given by Lynden-Bell and Katz is expressed in terms of Israel's theory of surface layers in general relativity. In this way an expression, valid for arbitrary radial coordinates, of the gravitational field energy in a static, spherically symmetric space-time, is deduced. This expression is applied to the Schwarschild and Reissner-Nordström space-times, and leads here to the same results as those given by Einstein's pseudotensor expression in isotropic coordinates.     

On a new variational principle in general relativity and the energy of the gravitational field

A new variational principle based on the affine connection in space-time is proposed. This leads to a new formulation of general relativity. The gravitational field is a field of inertial frames in space-time. The metricg appears as a momentum canonically conjugate to the gravitational field. In the case of simple matter fields, e.g., scalar fields, electromagnetic fields, Proca fields, or hydrodynamical matter, the new formulation is equivalent to the traditional one. A new formulation of conservation laws is proposed.     

The Electromagnetic Analogue of Some Gravitational Perturbations in Cosmology

Recently attention has been drawn to the fact that perfect fluid tensor perturbations (with perturbed vorticity and acceleration vanishing) of isotropic cosmological models have a perturbed Weyl tensor with electric part satisfying a linear, homogeneous, third-order wave equation while the magnetic part satisfies a linear, homogeneous, second-order wave equation. We construct an analogous class of electromagnetic test fields in the isotropic cosmological models for which the electric vector satisfies a third-order, linear and homogeneous wave equation while the magnetic vector satisfies a second-order, linear and homogeneous wave equation. If the perfect fluid has an equation of state we give a simplified derivation of the authors' previous perturbation analysis describing gravitational waves carrying arbitrary information. We also present the analogous solutions of Maxwell's equations which contain electromagnetic waves conveying arbitrary information.