The Pioneer anomaly in covariant theory of gravitation

2017

Preprint

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Abstract:In the weak-field approximation of covariant theory of gravitation the problem of 4/3 is formulated for internal and external gravitational fields of a body in the form of a ball. The dependence of the energy and the mass of the moving substance on the energy of field accompanying the substance, as well as the dependence on the characteristic size of the volume occupied by the substance are described. Additives in the energy and the momentum of the body, defined by energy and momentum of the gravitational and electromagnetic fields associated with the body are explicitly calculated. The conclusion is made that the energy and the mass of the body can be described by the energy of ordinary and strong gravitation, and through the energies of electromagnetic fields of particles that compose the body.

Section: Discussionmentioning

confidence: 90%

Section: It Follows Thatmentioning

confidence: 99%

Energy, Momentum, Mass and Velocity of a Moving Body

2017

Preprint

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“…Equations (46) are derived in [11] from the principle of least action and are similar in their form to Maxwell equations, which are used to calculate E and B . Finally, the charge density 0q  can be related to the velocity by means of the equation of the electric charge continuity: …”

Section: Discussionmentioning

confidence: 99%

“…According to the logic of the covariant theory of gravitation [11] and the metric theory of relativity [12], contribution to the definition of the system's metric is made by the stress-energy tensors of all the fields, including the gravitational field. The metric is a secondary function, the derivative of the fields acting in the system that define all the basic properties of the system.…”

Section: Equation For the Metricmentioning

confidence: 99%

Four-dimensional equation of motion for viscous compressible and charged fluid with regard to the acceleration field, pressure field and dissipation field

2015

Int. J. Thermo

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From the principle of least action the equation of motion for viscous compressible and charged fluid is derived. The viscosity effect is described by the 4-potential of the energy dissipation field, dissipation tensor and dissipation stress-energy tensor. In the weak field limit it is shown that the obtained equation is equivalent to the Navier-Stokes equation. The equation for the power of the kinetic energy loss is provided, the equation of motion is integrated, and the dependence of the velocity magnitude is determined. A complete set of equations is presented, which suffices to solve the problem of motion of viscous compressible and charged fluid in the gravitational and electromagnetic fields.Keywords: Navier-Stokes equation; dissipation field; acceleration field; pressure field; viscosity. IntroductionSince Navier-Stokes equations appeared in 1827 [1-2], constant attempts have been made to derive these equations by various methods. Stokes [3] and , in derivation of these equations, relied on the fact that the deviatoric stress tensor of normal and tangential stress is linearly related to the three-dimensional deformation rate tensor and the fluid is isotropic.Khmelnik [5] considered that Navier-Stokes equations are the extremum conditions of some functional, and a method of finding a solution of these equations is described, which consists in the gradient motion to the extremum of this functional.One of the variants of the four-dimensional stressenergy tensor of viscous stresses in the special theory of relativity can be found in book [6]. The divergence of this tensor gives the required viscous terms in the Navier-Stokes equation. The phenomenological derivation of this tensor is based on the assumed condition of entropy increment during energy dissipation. As a consequence, in the comoving reference frame the time components of the tensor, i.e. the dissipation energy density and its flux vanish. Therefore, such a tensor is not a universal tensor and cannot serve, for example, as a basis for determining the metric in the presence of viscosity.In this article, our goal is to provide in general form the four-dimensional stress-energy tensor of energy dissipation, which describes in the curved spacetime the energy density and the stress and energy flux, arising due to viscous stresses. This tensor will be derived with the help of the principle of least action on the basis of a covariant 4-potential of the dissipation field. Then we will apply these quantities in the equation of motion of the viscous compressible and charged fluid, and by selecting the scalar potential of the dissipation field we will obtain the NavierStokes equation. The essential element of our calculations will be the use of the wave equation for the field potentials

“…If we assume, as in [5]- [10], that all the fields appear and exist independently of each other, then the gauges of 4-potentials of the fields could also be independent of each other:…”

Section: The General Field Equationsmentioning

confidence: 99%

The Concept of the General Force Vector Field

2016

OALib

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A hypothesis is suggested that the fields associated with macroscopic bodies, such as classical electromagnetic and gravitational fields, acceleration field, pressure field, dissipation field, strong interaction field and weak interaction field, are the manifestations of a single general field. Using the generalized four-velocity as the four-potential of the general field, with the help of the principle of least action it is shown that each of these seven fields contributes linearly to the formation of the total four-force density. The general field equations, equation of the particles' motion in this field, equation for the metric and the system's energy are determined. It should be noted that the stress-energy tensor of the general field includes not only the stress-energy tensors of these seven fields, but also the cross terms with the products of various field strengths. As a result, the energy and momentum of the system with several fields can differ from the classical values, not taking into account such cross terms in the general field energy and momentum.