Gravitational Field Theory Research Articles

On the theory of gravitational field non-localized by the internal variable. - IV

In this paper, some structural considerations are developed on the concept of non-locality underlying the theory of gravitational field in Finsler spaces. In particular, the non-localization by the internal variable at a more microscopic level than the Finslerian one is considered in detail.

Evolution of a homogeneous isotropic universe, dark matter, and the absence of monopoles

It is shown that the field theory of gravitation leads to a unique scenario for the evolution of a homogeneous isotropic universe. It pulsates with time (with half-priod) ≅3.75×1010 yr between states with maximum (≅ 1067 g/cm3) and minimum (≅ 1.25× g/cm3) matter densities. The dark matter has a density about 25 times greater than the luminous matter. The maximum temperature corresponding to maximum matter density (∼1025°K ≅1012GeV) is insufficient for strong prodaction of monopoles (in a grand unified theory).

Theoretical Approach to Treatment of Non-Newtonian Forces

We consider the set of gravitational and unified field theories that predict the deviation on Newton's law. The main attention is paid to mechanisms of new forces origin and particles which can be regarded as the mediators of new type of interaction. The all known to us theories are divided into eight classes and relation and discrepancy between them are discussed

Toward a field theory of gravitation

A new theory of gravitation is presented in which the righ-hand side of the field equations contains the gravitational-field stress-energy tensort μ ν . The crucial new information leading to this construction is the demonstration that the two basic differential identities of space-time geometry (that of Bianchi and that of Freud) require atrue gravitational field stress-energy tensort μ ν which must be added to the matter tensor τ μ ν . Otherwise, the two identities clash and lead to a mathematical overdetermination which creates insurmountable internal difficulties for the curved-space-time theory of gravitation as a whole.

Hamiltonian structure of gravitational field theory

Hamiltonian generalizations of Einstein's theory of gravitation introducing a laminar structure of spacetime are discussed. The concepts of general relativity and of quasi-inertial coordinate systems are extended beyond their traditional scope. Not only the metric, but also the coordinate system, if quantized, undergoes quantum fluctuations.

Motion of a particle in the field of a rotating body in the post-Newtonian approximation. Alternative solutions

The components of the gravitational field are compared in the post-Newtonian approximation in the geometric (Einstein tensor) and field (Maxwellian vector form) theories of gravitation. The fundamental difference of these fields in the motion of a test particle is shown. The feasibility of qualitative detection of the vortex component of the gravitational field is found experimentally. The scheme for an alternate experiment is given.

Gravitation in 2+1 dimensions.

We investigate gravitational field theories in 2+1-spacetime dimensions. The consequences of the lack of a Newtonian limit to general relativity are reviewed. Further insight into the implications of this fact is gained by considering a new, general class of exact hydrostatic solutions. We show that all self-gravitating polytropic structures have the same gravitational mass and produce matter-filled spaces of finite spatial volume. Other theories of gravitation are also considered and the behavior of one such theory with a Newtonian limit is studied. Cosmological solutions of these gravitational theories are also studied in detail.

A theory of electromagnetic and gravitational fields

Careful calculations using classical field theory show that if a macroscopic ball with uniform surface charge (say, a billiard ball with 1E6 excess electrons) is released near the surface of the earth, it will almost instantaneously accelerate to relativistic speed and blow a hole in the ground. This absurd prediction is just the macroscopic version of the self-force problem for charged particles [1]. Furthermore, if one attempts to develop from electromagnetism a parallel theory for gravitational [2], the result is the same, self-acceleration. The basis of the new theory is a measure of energy density for any wave equation [3–5]. Given any solution of any four-vector wave equation in spacetime (for example, the potentials ( c -1 φA)=( A 0, A 1, A 2, A 3) in electromagnetism), one can form the 16th first order partial derivatives of the vector components, with respect to the time and space variables ( ct, x) = ( x 0, x 1, x 2, x 3). The sum of the squares of the 16 terms is a natural energy function [6, p. 283] (satisfying a conservation law ∂u ∂t = −▿ λ · S) . Such energy functions are routinely utilized by mathematicians as Lyapunov functions in the theory of stability of waves with boundary conditions. A Lagrangian using this sum leads to a new energy tensor for electromagnetic and gravitational fields, an alternative to that in [7].

Special relativistic gravitational theory

Based on special relativity, we introduce a way to develop a new field theory from (1) the relativistic property of the particle coupling coefficient with the field, and (2) the field due to a static point source. As an example, we discuss a theory of electromagnetic and gravitational fields. The results of this special relativistic gravitational theory for the redshift and the deflection of light are the same as those deduced from general relativity. The results of experiments on the planetary perihelion procession shift and on an additional “short-range gravity” are more favorable to the special relativistic gravitational theory than to general relativity. We put forward a new idea to test experimentally whether the equivalence principle of general relativity is correct.

A non-dualistic unified field theory of gravitation, electromagnetism and spin

The wisdom of classicalunified field theories in the conceptual framework of Weyl, Eddington, Einstein and Schrodinger has often been doubted and in particular there does not appear to be any empirical reason why the Einstein-Maxwell (E-M) theory needs to be geometrized. The crux of the matter is, however not whether the E-M theory is aesthetically satisfactory but whether it answers all the modern questions within the classical context. In particular, the E-M theory does not provide a classical platform from which the Dirac equation can be derived in the way Schrodinger's equation is derived from classical mechanics via the energy equation and the Correspondence Principle. The present paper presents a non-dualistic unified field theory (UFT) in the said conceptual framework as propounded by M. A. Tonnelat. By allowing the metric formds2=gμνdxvxv and the non-degenerate two-formF=(1/2> l)ϕμνdxv∧dxvto enter symmetrically into the theory we obtain a UFT which contains Einstein's General Relativity and the Born-Infeld electrodynamics as special cases. Above all, it is shown that the Dirac equation describing the electron in an “external” gravito-electromagnetic field can be derived from the non-dualistic Einstein equation by a simple factorization if the Correspondence Principle is assumed.

Quantization effects in the plasma universe

It is suggested that a unification of the morphology of the solar system, anomalous intrinsic red shifts of quasars and galaxies, the structure of the hydrogen atom, the Einstein equations of general relativity, and Maxwell's equations can be accomplished by a basic consideration of the minimum-action states of cosmic and/or virtual vacuum field plasmas. A formalism of planetary formation theory leads naturally to a generalization which describes relativistic gravitational field theory in terms of a 'pregeometry'. A virtual plasma associated with the vacuum state is postulated. It is demonstrated that the relaxed state of the virtual plasma underlies Einstein's field equation and predicts the proper form for the effective gravitational potential generated by the Schwarzschild solution of those equations. A further extension of the theory demonstrates that it also predicts the structure of the hydrogen atom described in terms of the Schrodinger equation of quantum mechanics. These concepts are applied in an attempt to explain the quantized anomalous red shifts in related galaxies as observed by H. Arp and J.H. Sulentic (1985). A possible unified field theory is suggested based on the above-mentioned concepts. >

The ?-field theory of gravitation and cosmology

The present paper presents, within the Einstein conceptual framework, a scalar field theory of gravitation. The Ω-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.

Symmetry Breaking Due to Conformally Invariant Scalar Field

AbstractIn the framework of Weyl invariant gravitational field theory including torsion coupled to a scalar field with arbitrary selfinteraction it will be shown that any solution of such a generalized Goldstone model contains the conformally invariant field of a massless scalar particle. Due to this fact it may happen that dynamical symmetry breaking becomes impossible.

Gauge fixing and renormalization in topological quantum field theory

We show how Witten's topological Yang-Mills and gravitational quantum field theories may be obtained by a straightforward BRST gauge fixing procedure. We investigate some aspects of the renormalization of the topological Yang-Mills theory. It is found that the beta function for the Yang-Mills coupling constant is not zero.

On the theory of gravitational field nonlocalized by the internal variable—III

Some physical considerations are made on Miron’ field equations, which are reconsidered as our field equations for the nonlocalized gravitational field from the fibre bundlelike standpoint. The gravitational field nonlocalized by the internal variable (w) is regarded as a unified field between the internal (w)-field and the external (x)-field, which corresponds to the total space of our fibre bundle. In this paper, different from the previous one, the dimension-reduction process, which maps the (w-field on the (x)-field, is not taken into account.

Gravitational radiation in Bianchi Type V cosmological models

This paper is concerned with the development of the theory of embedding gravitational radiation fields in expanding universes pioneered by Hawking. The problem of embedding such fields in the expanding Friedmann-Lemaitre-Robertson-Walker dust-filled universe, considered by Hawking, is reexamined in a new formalism which permits an easy analysis, in particular, of the relationship between the boundary conditions and the satisfaction, by the Weyl tensor, of the conventional peeling-off behavior. Since gravity wave detectors are expected to pick up plane-fronted gravitational waves, the main thrust of this paper concerns the development of a formulation of Bianchi Type V cosmological models which enables the embedding of such plane-fronted waves to be carried out. This is worked out explicitly in the case of a perfect fluid, with pressure proportional to energy density, and with the histories of the fluid particles orthogonal to the surfaces of homogeneity. 18 references.

New Weyl theory: Geometrization of electromagnetism and gravitation: Motivations and classical results

A geometrical unified field theory of electromagnetism and gravitation is developed in a Weyl space-time. The integrability conditions of the field equations cast the laws of classical perfect fluids under electromagnetic interactions. The purely gravitational limit of the theory is Einstein's General Relativity and the purely electromagnetic case coincides with the predictions of Maxwell's theory.

On the theory of gravitational field nonlocalized by the internal variable

On the theory of gravitational field nonlocalized by the internal variable

On the Theory of Gravitational Field in Finsler Spaces

AbstractSome structural considerations are made on the Finslerian gravitational field: A Finslerian metrical structure such as gλχ(x, y) = γλχ(x) + hλχ(x, y) is proposed, where γλχ denotes the Riemann metric of Einstein's gravitational field, while hλχ the Finsler metric induced by the Riemann metric hij(y) of the internal field; The intrinsic behaviour of the internal variable y, which is expressed as ȳi = K(x, y) yj in the internal field, is grasped by the Finslerian parallelism δyi (=0), which is reflected in the spatial structure of the external gravitational field by the mapping relation δyχ = e(x) δyi. The whole metrical Finsler connection D for gλχ(i.e., Dgλχ = 0) is determined by taking account of the intrinsic behaviour δyχ.

Gravitation, the general theory of relativity, and alternative theories

The main stages in the construction of the theory of gravitation and prospects for its further development are discussed. The main attention is devoted to comparing the properties of the relativistic gravitational field and other physical fields. Two equivalent formulations of the general theory of relativity—the geometrical and the field— are considered in detail. It is explained why some of the field theories of gravitation developed in flat space-time are not different theories of the relativistic gravitational field but merely other formulations of general relativity.