Extended translational invariance and the tetrad theory of gravitation

A tetrad theory of gravitation is derived systematically from the requirement of localization of the group of translations. It is shown that when the sources of the gravitational field are chosen in the form of the total canonical energymomentum tensor of the nongravitating matter this gauge theory is identical with the previously formulated tetrad theory of gravitation in a space of absolute parallelism.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 137–141, April, 1977.     

Gravitation and compensating fields

The compensation approach to gravitation is considered. A general method of compensating fields for an arbitrary Lie group is expounded. The geometrical and physical interpretation is given. In the special case of the Lorentz group, a theory of gravitation is constructed.     

Averaged Lagrangians and MacCallum-Taub's limit in macroscopic gravity

The derivation of MacCallum-Taub's averaged high-frequency Lagrangian [1] is analysed with special attention paid to the assumptions made along the derivation. It is shown that averaged high-frequency Lagrangians of the same form as MacCallum-Taub's Lagrangian can be derived by applying the Brill-Hartle and macroscopic gravity averaging schemes. A procedure for the derivation of a Lagrangian of macroscopic gravity (an averaged Hilbert action) is proposed and its high-frequency limit (namely, its high-frequency perturbation expansion up to the second order terms in perturbations, which is referred to as MacCallum-Taub's limit) is calculated. There is disagreement [2] in the expressions for MacCallum-Taub's averaged high-frequency Lagrangian and the high-frequency limit of the macroscopic gravity Lagrangian. Possible reasons for such disagreement are analysed. The origin of the difference is shown to consist in using the propagation equation for perturbations, i.e. the linearized Ricci tensor vanishes, during the derivation (averaging) carried out in [1]. A new derivation of an averaged high-frequency Lagrangian without assuming the propagation equation to hold and by taking into account the proper correlation functions is given. The newly derived expression is shown to coincide with MacCallum-Taub's limit of the macroscopic gravity Lagrangian, which resolves the disagreement.     

Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum tensor

The microscopic and the macroscopic (phenomenological) approach to the electromagnetic theory in matter can be looked upon as complementary to each other. In view of the complexity of the deductive microscopic approach it is desirable to use experimental information to test the predictions of the more simple macroscopic theory. The purpose of the present paper is to review and give the theory of experiments and Gedanken experiments in relation to various expressions for the electromagnetic energy-momentum tensor. The paper is divided into three parts. The first part discusses the electrostriction effect, mainly in electrostatic experiments. It turns out that both the Hakim-Higham experiment (1962) and the Goetz-Zahn experiment (1958) agree with the predictions of the Helmholtz theory and disagree with the predictions of the Einstein-Laub theory. The second part of the paper is concerned with quasi-stationary crossed electric and magnetic fields. The electrostriction effect is here unimportant. Both the experiment of Walker et al. (1975) and that of James (1968) support the Abraham tensor in contradiction to the Minkowski tensor. The third and most extensive part of the paper discusses optical phenomena, in which case a direct observation of the fluctuating Abraham force cannot be made. Under usual circumstances, it turns out to be simplest to use the divergence-free Minkowski tensor. This tensor describes satisfactorily all existing force or torque experiments in optics that we are aware of. Some attention is given also to the tensor alternative recently introduced by Peierls (1976).     

Spherically symmetric fields in Rosen's bimetric theories of gravitation

By means of bimetric Killing vectors two spherically symmetric fields are investigated: (i) the time-dependent one in Rosen's flat-background bimetric theory; and (ii) the energy-preserving in Rosen's cosmological-background bimetric theory withk = 1. In the first case a wave behavior of the field is present. In the second case a time evolution is obtained for fields, created by insular systems of constant energy. These phenomena are typical for bimetric theories of gravitation.     

Equations of motion in Rosen's bimetric theory of gravitation

The paper contains an investigation of Rosen's bimetric theory of gravitation in the case of slow velocities and weak fields. Newtonian and post-Newtonian approximations are obtained. The post-Newtonian equation of motion is integrated for an insular system of spherical bodies that move translationally at large mutual distances. It appears that the post-Newtonian law of motion obtained in this way contains terms that depend on the self-energy of the test body (a self-influence phenomenon). It is proved that also in the Einsteinian gravitation this influence is present, but it can be canceled out from the post-Newtonian law of motion if one takes into account the de Donder conditions. The self-influence discovered here seems to be a general gravitation phenomenon, which usually appears in theories of gravitation in the post-Newtonian approximation.     

The velocity of gravitational waves

We examine the propagation of gravitational waves in the new field theory of gravitation recently proposed by Novello-De Lorenci-Luciane (NDL). This examination is done on a solvable case corresponding to a spherically symmetric static configuration. We show that in NDL theory the velocity of gravitational waves is lower than light velocity. We point out some consequences of this result and suggest a possible scenario for its verification.     

Power-Law Expansion and Scalar Field Cosmology in Higher Derivative Theory

In this paper we study the evolution of a flat Friedmann-Robertson-Walker model filled with a perfect fluid and a scalar field minimally coupled to gravity in higher derivative theory of gravitation. Exact solution of the field equations are obtained by the assumption of power-law form of the scale factor. A number of evolutionary phases of the universe including the present accelerating phase are found to exist with scalar field in the higher derivative theory of gravitation. The properties of scalar field and other physical parameters are discussed in detail. We find that the equation of state parameter for matter and scalar field are same at late time in each case. We observe that a higher derivative term can hardly be a candidate to describe the presently observed accelerated expansion. It is only the hypothetical fluids, which provide the late time acceleration. It is also remarkable that the higher derivative theory does not effect the radiating model of scalar field cosmology.     

A quantum theory of higher virial coefficients

Recently a theory of time-delay phenomena in few particle scattering has been developed. The results of this theory are used to investigate the quantum virial coefficient problem in the case of Boltzmann statistics. Working within the frame work of Faddeev's time-dependent scattering theory we find explicit formulas for the higher virial coefficients. One aim of statistical mechanics is to derive all the equilibrium properties of a macroscopic system from the dynamical laws of the constituent particles. Our solutions for the higher virial coefficients prove that the macroscopic properties of a quantum gas are sensitive only to the time-delay aspect of the collision process. The analysis does not restrict the type of interactions between the constituents with the one exception of long-range Coulomb forces. In particular, the interaction may be attractive and strong enough to form stable few-particle clusters. Thus our solution describes the equilibrium in a quantum gas where the interactions are responsible for creating different species types.     

Linearized gravitation theory in macroscopic media

The refraction of gravitational waves is discussed by developing a macroscopic theory of gravitation along the lines of classical electromagnetism. It is shown that the linearized Bianchi identities may be expressed in a form which is suggestive of Maxwell's equations with magnetic monopoles. The medium is then assumed to be corpuscular in structure and it is shown how, on performing an averaging process on the field quantities, the Bianchi identities must be modified by the inclusion of polarization terms resulting from the induction of quadrupole moments on the individual “molecules”. A model of a medium whose molecules are harmonic oscillators is discussed and constitutive equations are derived. Gravitational waves are demonstrated to slow down in such a medium.     

Gravitation in flat space-time

A previously studied Lorentz-covariant theory of gravitation is given in generally covariant form, i.e., the theory holds for arbitrary reference frames. Flat space-time is a natural condition for the conservation of energy and momentum. The energy-momentum tensor of matter and gravitation is the source of the gravitational field.     

Strong gravitation waves in terms of Maurer-Cartan forms

Strong gravitation plane waves are represented in terms of the Maurer-Cartan spin connection coefficients in cosmological background. It was shown that the diffeo-invariance of spin connection coefficients leaves only one degree of freedom of the strong gravitation plane waves in contrast to the metric approach, where gravitation waves have two degrees of freedom like photons in QED. The Hilbert action of gravitation waves in terms of spin connection coefficients takes the form of a bilinear field theory.     

Weak circulation theorems as a way of distinguishing between generalized gravitation theories

We proved in a previous paper that a generalized circulation theorem characterizes Einstein's theory of gravitation as a special case of a more general theory of gravitation, which is also based on the principle of equivalence. Here we pose the question of whether it is possible to weaken this circulation theorem in such ways that it would imply more general theories than Einstein's. This problem is solved. Principally, there are two possibilities. One of them is essentially Weyl's theory.     

Einstein: Distant parallelism and electromagnetism

Einstein's approach to unified field theories based on the geometry of distant parallelism is discussed. The simplest theory of this type, describing gravitation and electromagnetism, is investigated. It is found that there is a charge-current density vector associated with the geometry. However, in the static spherically symmetric case no singularity-free solutions for this vector exist.     

The gravitational interaction: Spin,rotation, and quantum effects-a review

Previous work on spin, rotation, and quantum effects in gravitation is surveyed, with particular emphasis on the gravitational two-body interaction, both for elementary particles and for macroscopic bodies. Applications considered include (a) the precession of a gyroscope, (b) rotational effects on the equations of motion for the orbit, (c) binary systems, particularly the binary pulsar PSR 1913+16, and (d) the prospects of measuring spin-orbit and spin-spin forces in the laboratory. In addition, we discuss quantum effects that arise in the interaction between elementary particles. In particular, we point out the potentially decisive role of these forces in high-density matter, with emphasis on the fact that repulsive forces arise that may prevent gravitational collapse. All of the above considerations are within the framework of Einstein's theory of general relativity, albeit extended to treat spin-dependent and quantum forces. Finally, we consider the additional quantum terms that are present if one works with a generalization of Einstein's theory, the Einstein-Cartan-Sciama-Kibble theory of gravitation, in which the spin of matter, as well as its mass, plays a dynamical role.     

Massive Yang-Mills Field Theory with Conformal (Weyl) Invariance

A massive Yang-Mills field theory with the conformal (Weyl) invariance^[1] and gauge invariance is proposed. It involves the gravitational and various gauge interactions, in which all the mass terms appear as the uniform interactional form m(x) = KΦ(x). When the conformal and gauge symmetries are broken spontaneously, the Einstein gravitation emerges and all the fields obtain masses, this theory is renormalizable and unitary with the gravitation ignored. Finally we give a relation between the theory and the Higgs mechanism.     

Exact Plane-Wave Solution of the Equations of a Theory of Gravitation with a Massive Graviton

Russian Physics Journal - A theory of gravitation with a massive graviton which was proposed by Visser is considered. An exact solution of this theory is found for the case when the source of the...