A non-covariant theory of gravitation,II

This is a continuation of a previous paper, in which a theory of gravitation was developed based on the existence of a preferred frame of reference and a preferred time coordinate in the universe. The gravitational field equations are derived with the help of a variational principle containing three constants. Two relations among the constants are introduced, leaving one of them arbitrary. This constant does not affect the precession of the perihelion of Mercury but does affect the behaviour of gravitational waves. By changing one of the relations among the constants, one can account for the discrepancy in the precession of the perihelion associated with the oblateness of the sun, as found by Dicke and Goldenberg.     

A bi-metric theory of gravitation

A bi-metric theory of gravitation is proposed, satisfying the covariance and equivalence principles. It is based on a simple form of Lagrangian and has a simpler mathematical structure than that of the general theory of relativity. The theory agrees with general relativity up to the accuracy of the observations made up to now. The static spherically symmetric solution of the present field equations does not involve any 'black hole'.     

Already unified field theory with non-covariant geometrization

In general relativity the non-covariant ansatzA ⁱ = ₄ ⁱ for the vectorpotentialA _k gives the general solution of the Maxwell equations as four coordinate conditions which are the conditions of integrability of the Einstein equations. In the some sense the ansatz=X ⁴ is a general solution of the scalar wave-equation in a reference system given by one coordinate-condition. We discuss the meaning of the canonical quantization of the fields in such reference systems.     

A scalar field theory of gravitation

A scalar theory of gravitation is developed from a variational principle. The speed of light is taken to be a function of the potential of the gravitational field. The predictions of the light deflection and the advancement of the perihelion agree with those made by Einstein's theory. The gravitational (active) mass differs from the inertial (passive) mass and both are dependent on the gravitational potential.     

Gauge gravitation theory

The particularity of the gauge gravitation theory is that Dirac fermion fields possess only Lorentz exact symmetries. It follows that different tetrad gravitational fieldsh define nonisomorphic representations _h of cotangent vectors to a space-time manifoldX ⁴ by Dirac's-matrices on fermion fields. One needs these representations in order to construct the Dirac operator defined in terms of jet spaces. As a consequence, gravitational fieldsh fail to form an affine space modeled after any vector space of deviationsh'–h of some background fieldh. They therefore fail to be quantized in accordance with the familiar quantum field theory. At the same time, deformations of representation _h describe deviations ofh such thath + is not a gravitational field. These deviations form a vector space, i.e., satisfy the superposition principle. Their Lagrangian, however, differs from familiar Lagrangians of gravitation theory. For instance, it contains masslike terms.     

A bi-metric theory of gravitation. II

The bi-metric theory of gravitation proposed previously is simplified in that the auxiliary conditions are discarded, the two metric tensors being tied together only by means of the boundary conditions. Some of the properties of the field of a particle are investigated; there is no black hole, and it appears that no gravitational collapse can take place. Although the proposed theory and general relativity are at present observationally indistinguishable, some differences are pointed out which may some day be susceptible of observation. An alternative bimetric theory is considered which gives for the precession of the perihelion 5/6 of the value given by general relativity; it seems less satisfactory than the present theory from the aesthetic point of view.     

A coupled theory of electromagnetism and gravitation

A coupling electromagnetism with a previously developed scalar theory of gravitation is presented. The principle features of this coupling are: (1) a slight alteration to the Maxwell equations, (2) the motion of a charged particle satisfies an equation with the Lorentz force-appearing on the right side in place of zero, and (3) the energy density of the electromagnetic field appears in the gravitational field equation in a manner similar to the mass term in the Klein-Gordonequation. The field of a static, spherically symmetric charged particle is computed. The electromagnetic field gives rise to l/r ² terms in the gravitational potential.     

Matrix theory of gravitation

A new classical theory of gravitation within the framework of general relativity is presented. It is based on a matrix formulation of four-dimensional Riemann-spaces and uses no artificial fields or adjustable parameters. The geometrical stress-energy tensor is derived from a matrix-trace Lagrangian, which is not equivalent to the curvature scalar R. To enable a direct comparison with the Einstein-theory a tetrad formalism is utilized, which shows similarities to teleparallel gravitation theories, but uses complex tetrads. Matrix theory might solve a 27-year-old, fundamental problem of those theories (Sect. 4.1). For the standard test cases (PPN scheme, Schwarz schild-solution) no differences to the Einstein-theory are found. However, the matrix theory exhibits novel, interesting vacuum solutions.     

Lorentz-Covariant theory of gravitation

A Lorentz-covariant theory of gravitation is proposed. It is based on a simple form of the Lagrangian for the gravitational field. The field equations have a simple mathematical structure where the energy-momentum tensor of matter and of gravitational field is the source of the field. The theory agrees with general relativity for the three well-known effects, i.e., red shift, deflection of light, and perihelion.     

Higher-order theory of gravitation

The field equations obtained by introducing a correction in the Hubert Lagrangian in the form of a series of finite terms inR (g R ) are considered in order to study the implications for the cosmological singularity.     

Relativistic theory of gravitation

In the present paper a relativistic theory of gravitation (RTG) is unambiguously constructed on the basis of the special relativity and geometrization principle. In this a gravitational field is treated as the Faraday-Maxwell spin-2 and spin-0 physical field possessing energy and momentum. The source of a gravitational field is the total conserved energy-momentum tensor of matter and of a gravitational field in Minkowski space. In the RTG the conservation laws are strictly filfilled for the energy-momentum and for the angular momentum of matter and a gravitational field. The theory explains the whole available set of experiments on gravity. By virtue of the geometrization principle, the Riemannian space in our theory is of field origin, since it appears as an effective force space due to the action of a gravitational field on matter. The RTG leads to an exceptionally strong prediction: The universe is not closed but just flat. This suggests that in the universe a missing mass should exist in a form of matter.     

Generalized theory of gravitation

The mathematical formulation of the nonsymmetric gravitation theory (NGT) as a geometrical structure is developed in a higher-dimensional space. The reduction of the geometrical scheme to a dynamical theory of gravitation in four-dimensional space-time is investigated and the basic physical laws of the theory are reviewed in detail.     

A geometrical property of action in gravitation theory

It is shown that in regard to the special spacial foliation associated with the gas of a standard clock, the action of gravitation theory is proportional to the time parameter, while the coefficient of proportionality is equal to the energy of the gravitational field and other fields in the reference system formed by the gas of the standard clock.St. Petersburg State Technical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 81–84, November, 1993.     

A background-dependent approach to the theory of gravitation

On the basis of a Machian view of nature we find a covariant formulation of Newton's gravitational equation in a general frame which satisfies the requirements (i) of being singular if the density of mass is zero everywhere and (ii) of depending on the parallel transport of the four-momentum density of matter (from the three-space point in which it is defined to any other three-space point, at any fixed time) in such a way that it incorporates the idea that the frame has to be fixeddirectly in connection with the distribution and motion of matter. In Paper II we will use such an equation as starting point in order to find relativistic gravitational equations which are supposed to hold in any conceivable universe, describe a purely geometrical theory of gravitation, and explicitly incorporate Mach's principle.     

A spin-3/2 theory of gravitation

Stimulated by ideas occuring in supergravity, we develop a gauge theory of gravity based on a spin-3/2 Majorana field. Our theory has no metric or vierbein as an elementary field. Classically the theory is in complete agreement with Einstein's metric formulation, but quantum mechanically it differs from ordinary formulations, including supergravity, on the fundamental nature of gravitation. In our approach gravitation arises from a collective effect due to spin-3/2 gravitinos.This essay was awarded the fifth prize for 1978 by the Gravity Research Foundation. (Ed.) Research supported in part by the Department of Energy under contract number EY-76-C-02-3075-190.Alfred P. Sloan Foundation Fellow.     

Many-time hamiltonian gravitation theory

It is shown that given any “good” coordinate condition in Hamiltonian general relativity one can construct an associated many-time formulation in which the constraints can be solved for some of the momenta as functionals of the remaining canonical variables. Since good coordinate conditions appear to be available for both open and closed spaces it follows that the functional wave equation for general relativity can be always put in a Tomonaga-Schwinger form. The implications of this result and some open problems are briefly discussed.     

A spontaneously broken conformal gauge theory of gravitation

In a fusing of a few attractive ingredients, we consider a spontaneously broken conformal gauge theory of gravitation, with an underlying Riemann-Cartan-Weyl geometry. The theory contains no intrinsic dimensional parameters, is unitary, and has the Schwarzschild metric as the unique spherically symmetric solution of the vacuum field equation (thus guaranteeing agreement with observed gravitational phenomena). The particle content of the theory consists of a massless 2^. graviton, and a super-massive 1^? “conformon”.     

On Sakharov's theory of gravitation

The Sakharov theory of gravitation is examined from the viewpoint of the analogy between gravitation and elasticity. It is found that, by using the Cattaneo-Zel'manov projection technique, the deformation tensor connected with the gravitational field can be considered the deformation tensor of a suitable elastic medium. By supposing that transversal waves propagate in this medium with velocityc, one can find an explicit expression for the time dependence of the gravitational constant. Some applications of cosmological interest are briefly discussed.