The Ω-field theory of gravitation and cosmology

The present paper presents, within the Einstein conceptual framework, a scalar field theory of gravitation. The -field, however, is not superimposed on the space-time manifold from outside the given geometry but is derived from the space-time torsion which is shown to be the generator of gravitation and inertia as well as spin. The theory predicts the three crucial tests of gravitation to the same degree of accuracy as does Einstein's theory. But it also predicts gravitational radiation emitted by a pulsating sphere and a singularity free cosmology in contradiction to Einstein's results. Above all, the scalar gravitational field can be easily quantized in the present context.     

Nonlinear gravidynamics: Energy-momentum tensor of collapsar field

In the bounds of a theoretical scheme treating consistently gravitational interaction as dynamical (gauge) field in flat space-time, an expression was obtained for the density of energy-momentum-tension of gravitational field in vacuum around a collapsed object. A case was studied of an interacting static spherically-symmetric field of a collapsar in vacuum with taking into account of input of all the possible components (spin states of virtual gravitons) into the energy for the symmetric tensor of second rank _ik . The radius of the sphere filled by matter for the collapsar of massM may achieve values up toGM/c ².     

On birkhoff’s theorem in the bimetric scalar-tensor theory of gravitation

It is shown that in the most general version of the bimetric scalar-tensor theory of gravitation, a spherically symmetric vacuum gravitational field is static if the gravitational scalar does not depend on time. This result is generalized to certain cases in which a source is present, including an electromagnetic field. Both branches of solutions with a variable and a constant scalar field are considered. Translated from Astrofizika, Vol. 40, No. 2, pp. 281–290, April–June, 1997.     

Axisymmetric stationary vacuum fields in the general scalar tensor theory

It is show that axisymmetric stationary vacuum solutions of the general scalar tensor theory of gravitation proposed by Nordvedt and later discussed by Barker and others can be obtained from the solutions of the axisymmetric stationary Einstein vacuum fields and also from the axisymmetric static vacuum fields of the general scalar tensor theory. The scalar tensor analogue of the Kerr solution has been obtained.     

Exact cosmological solutions in the scalar-tensor theory with cosmological constant

Under the assumption of a power-law between the expansion factor of the Universe, and the scalar field (a ⁿ=c=const.) tensor theory with cosmological constant are reduced to quadrature. Several exact solutions are obtained, among them inflationary universes that have barotropic equation of state.     

The universal solution of Einstein's equations of general relativity

Einstein's equations of general relativity are solved in terms of gravitational potential derivatives, withT equal to mass and/or field energy such thatT 0 outside a body. The line element equation then describes the variance of test particle internal geometrical structure and time-rate due to work done in a field, not the space-time curvature. Specific properties of gravitational fields and bodies come from this new solution: (a) The gravitational field consists of electromagnetic spin 2 gravitons which produce the gravitational force through the magnetic vector. (b) The gravitational mass is the Newtonian mass, not the relativistic mass, of a moving body. (c) An action principle exists in gravitation theory. (d) Attractive gravity exists between matter and antimatter. (e) Unification with quantum physics appears possible.     

The millisecond pulsar and neutron star structure

Rotational stability condition is applied to the PSR 1937+214 pulsar, suggesting that its rapid rotational rate may be close to the limit of rotational stability. This application implies additional bounds on the mass, radius, and moment of inertia of neutron star models, which depend on the theory of gravitation and the equation of state of cold superdense matter. Results obtained for various equations of state and theories of gravitation are used to set limits on the surface magnetic field and slow down rate of pulsar models.     

The time-dependent problem in the Jordan-Brans-Dicke tensor-scalar theory of gravitation

We state the time-dependent problem in the Jordan-Brans-Dicke tensor-scalar theory of gravitation. We show that in the conformally corresponding space the equations of the problem have the same form as the Einstein equations with an extra source in the form of the components of the energy-momentum tensor of the scalar field. We discuss the question whether Birkhoff's theorem can hold in the Jordan-Brans-Dicke theory. We simultaneously obtain a formula that expresses the mass of an isolated static object as a function of the distribution of pressure of matter. We also discuss the integrability of the vacuum time-dependent equations of the Einstein theory.Translated fromAstrofizika, Vol. 37, No. 3, 1994.The authors are grateful to the participants in the seminar of the Department of Theoretical Physics of Erevan State University for helpful discussions. Two of the authors (VVP and GGA) worked with partial support from grant RY 6000 of the International Science Fund (Soros Foundation).     

A cosmological model without singularity

Based on the assumption, that potential energy of matter in a mass filled space contributes a negative term to the energy tensor, solutions of the Einstein field equations are possible that exhibit no singularities, since the action of gravity changes sign when the density of potential energy exceeds the density of mass-energy. The solution, in which potential energy and mass-energy are in balance, is identical with Einstein's static universe. It is shown that all the observational facts, that are usually considered as confirming the big bang model, as the cosmological red shift, the abundances of light elements and the existence of the microwave background radiation, can be understood also in a static world model, when it is taken into account that due to the finite velocity of gravitational interaction all moving quanta lose momentum to the gravitational tensor potential. As in the static cosmological model the overwhelming fraction of the total mass exists in form of a hot intergalactic plasma. The model gives a simple explanation for the diffuse x-ray background and a solution to the missing mass problem without invoking any kind of new physics or of yet undiscovered particles. Also the causality problem and the curvature problem posed by the energy density of the quantum mechanical vacuum fields find a natural solution.     

A nonlinear tensor field and the second metric tensor

In our preceding paper {see [L. Sh. Grigorian and S. Gottlöber, Astrofizika (in press)]} we investigated a self-gravitating system consisting of a scalar field and a linear tensor field _ik= _ki with minimal coupling and with allowance for the action of vacuum polarization effects. In the present paper we investigate the case of a nonlinear tensor field _ik. The action S ⁽⁾ of the field _ik is determined by the difference R_ik — _ik, where R_ik is the space-time Ricci tensor and Rik is the analogous quantity constructed using the metric _ik=g_ik+_ik induced by _ik ( is a free parameter). Here S ⁽⁾ coincides with the previously known expression for the action of a linear field _ik. Equations of motion are derived for _ik in curved space-time. The energy-momentum metric tensor, determining the contribution of _ik to the gravitational field equations, is calculated.Translated from Astrofizika, Vol. 39, No. 1, pp. 135–144, January-March, 1996.     

Gravitational interaction of bodies immersed in fluids

It is shown that Archimedes' principle can be generalized for external gravitational fields due to stationary macroscopic bodies. For instance, a particle immersed in a homogeneous fluid at the centre of spherical symmetry of the fluid, or anywhere in an unbounded homogenous fluid, experiences — in an external field — a force that it would experience in a vacuum if it had an apparent mass less than the actual one by the mass of displaced fluid. Inversely, if one immerses a particle into a symmetrically arranged homogeneous fluid apart from its centre of symmetry, the particle and the fluid produce, at the centre of symmetry of the fluid, a gravitational field that would be produced in vacuo by a particle of the same size and shape but having apparent mass. Simple laboratory experiments, suitable to verify this inverse theorem, are described. On the other hand, the gravitational force between two particles in an infinite homogeneous fluid is reduced by a factor proportional to the product of their apparent masses which can be positive or negative. Two particles with opposite apparent masses repel each other. The results obtained imply corrections to vacuum of the order of (10^–5–10^–4) G of the gravitational constant,G, measured by the common laboratory methods.     

Solar radio spectra between 160 and 320 MHz

Dynamic spectra of incremental solar radio emission reveal that (mostly faint) pulsating and morphologically similar structures, including patterns of bright spots, dominate between ca. 250 and 320 MHz. As individual bursts these bright spots are similar to Type I bursts but they appear in an entirely different environment. This kind of activity is indicative of Type IV emission and seems to favour the generation of Type III bursts. Often its boundary with storm activity at the lower side of the band is rather sharp.     

Density perturbations in the Brans-Dicke theory

We give here the calculation of density perturbations in a gravitation theory with a scalar field non-minimally coupled to gravity, i.e., the Brans-Dicke theory of gravitation. The purpose is to show the influence of this scalar field on the dynamic behaviour of density perturbations along the eras where the equation of state for the matter can be put under the formp=, where is a constant. We analyse the asymptotic behaviour of this perturbations for the cases =0, =–1, =1/3 and =0. In general, we obtain a decaying and growing modes. In the very important case of inflation, =–1, there is no density perturbation, as it is well known. In the vacuum phase the perturbations on the scalar field and the gravitational field present growing modes at the beginning of the expansion and decaying modes at the end of this phase. In the case =0 it is possible, for some negative values of , to have an amplification of the perturbations with a superluminal expansion of the scale factor. We can also obtain strong growing modes for the density contrast for the case where there is a contraction phase which can have physical interest in some primordial era.     

Inflationary solutions for anisotropic model in scalar-tensor theory

In this paper we have studied B-D theory and general scalar tensor theory of Gravitation for anisotropic cosmological model in the false vacuum state. The possibility of both exponential inflation and power function inflation are examined for constant or variable coupling parameter . Also asymptotic limit of the scalar field and are discussed.     

Cosmological models in semi-classical and higher order gravitational theories

We have studied semiclassical models with a classical scalar field, givingexact solutions in the cases of a ⁴ and an exponentialself-interaction potential, in the last case we have also studied theinfluence of the vacuum polarization terms on the stability of the power-lawsolutions. We have also found cosmological exact solutions to the higherorder gravitational equations derived from a Lagrangian with a R ^k Rstructure, and investigated the stability of the de Sitter and Minkowskispace-time in the sixth order approximation of this theory.     

Exact solutions of a flat cosmological model in BSTT

We solve the cosmological equations for the bimetric scalar—tensor theory of gravitation (BSTT) for a flat model of the Friedmann type with the equation of state p = a. In the initial stage of expansion, the energy density of the scalar field dominates over the energy density of matter. As a result, the behavior of the solution in this limit does not depend on a. For later stages of expansion of the Universe, the solution obtained goes to a special solution having the form of a power law function of time. In this case, the relative change in the gravitational scalar is proportional to the Hubble parameter. In the limit of large values for the parameter of the theory, only a simple solution with zero value of the constant of integration goes to the corresponding Friedmann solution of general relativity theory.Translated from Astrofizika, Vol. 37, No. 2, pp. 351–362, April–June, 1994.I would like to thank L. Sh. Grigoryan for valuable discussions and support.     

The properties of the strong static field of a collapsar in gravidynamics

In the bounds of the totally nonmetric model of gravitational interaction theory (gravidynamics) the strong field of a compact object (a collapsar) — an analogue to the black hole in general relativity — is investigated. In the case of utmost strong (for gravidynamics) collapsar, field a region filled, by matter (a bag) must have the radius equal tor _*=GM/c ² 10 km at the total collapsar massM7M . Only half of the collapsar mass is contained in the bag, the other one of its total energy (Mc ² ) is distributed in the space surrounding the bag in the form of a coat, i.e., in the form of continuous medium (a relativistic gas) of virtual gravitons. The object must have the surface (the bag surface) with absolutely definite physical properties. The potential of such a surface is finite (₊=-c ²/2) and the particle mass finding itself in a bound state on the bag surface is two times less than the mass of the same particle in a totally free state. The bag surface can perform periodic oscillations (pulsations) with the periodGM/c ² 3×10^–5 s. An energy density inside the bag with the utmost strong gravitational field or with an utmost dense coat shrouding the bag is determined by gravitation theory constants only and depends on the distance to the bag centerr in the following way: (r)=(c ⁵ /8G)r ^–2. The bag matter in the case is most probably in the state of quark-gluon plasma.     

Radiative transfer in a homogeneous magnetized plasma

On the ground of the proper wave representation the general theory is developed of radiative transfer in a homogeneous plasma with the strong magnetic field ( _B /1). The linear and nonlinear equations are derived which generalize the corresponding equations of scalar radiative transfer theory in isotropic media. The solutions of some problems are given for the cases when the magnetic field is perpendicular to the surface: diffuse reflection of radiation from a semiinfinite medium, provided the sources are placed far from the surface (Milne's problem) and have constant intensity, increase linearly or quadratically with the optical depths, or decrease exponentially from the surface.     

Electromagnetic Brans-Dicke-Bianchi type-V solutions

We derive new solutions for the locally rotational-symmetric Bianchi type-V space-time in the Brans-Dicke theory of gravitation. The solutions represent anisotropic cosmological models filled with stiff matter and an electromagnetic null field, including the vacuum case. It is shown that the scalar field is dynamically an essential factor, since it influences the structure of the singularities and the expansion of the models.