The General Equation of Motion in a Gravitational Field Based Upon the Golden Metric Tensor (original) (raw)
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Second Approximation of the Generalized Planetary Equation Based upon Golden Metric Tensors
Journal of High Energy Physics, Gravitation and Cosmology
In this paper, we consider the Post Einstein Planetary equation of motion. We succeeded in offering a solution using second approximation method, in which we obtained eight exact mathematical solutions that rebel amazing theoretical results. To the order of C −2 , two of these exact solutions are reduced to the approximate solutions from the method of successive approximations.
International Journal of Theoretical & Computational Physics, 2021
Golden metric tensors exterior to hypothetical distribution of mass whose field varies with time and radial distance have been used to construct the coefficient of affine connections that invariably was used to obtained the Einstein's equations of motion for test particles of non-zero rest masses. The expression for the variation of time on a clock moving in this gravitational field was derived using the time equation of motion. The test particles in this field under the condition of pure polar motion have an inverse square dependence velocity which depends on radial distance. Our result indicates that despite using the golden metric tensor, the inverse square dependence of the velocity on radial distance has not been changed.
Notes on Geometric to Kinematic Expression of the Gravitational Field Equations
In 1980, I began a study of the kinematic expression of Einstein's geometric gravitational field equations. The binder containing my handwritten notes on this study had been laying on a bookshelf, forgotten for 37 years. So far, I have transcribed only the first 32 equations of the work. The balance of the work has yet to be deciphered from the haphazard notes of the second half, which explored the hyperbolic nature interaction of the field with the "space-time" medium. Those notes were entered in while travelling on public transportation between projects during my earlier career as an independent technologist. This work does not have a discussion capacity as I believe it should pertain to the current collaborative work discussion: "UNCHARTED TERRITORY - A Voyage of Discovery into the Geometry and Substance of Our Universe". I will add to this collection of notes as I "translate/decipher" them from my original writings.
Physics Essays, 2021
In general relativity, the values of constant terms in the equations of motions of planets and light have not been seriously discussed. Based on the Schwarzschild metric and the geodesic equations of the Riemann geometry, it is proved strictly in this paper that the the constant term in the time-dependent equation of motion of planet in general relativity must be equal to zero. Otherwise, when the correction term of general relativity is ignored, the resulting Newtonian gravity formula would change its basic form. Due to the absence of this constant term, the equation of motion can not describe the elliptical and the hyperbolic orbital motions of celestial bodies in the solar gravitational field. It can only describe the parabolic orbital motion (with minor corrections). Therefore, it becomes meaningless to use general relativity calculating the precession of Mercury's perihelion. It is also proved that the time-dependent orbital equation of light in general relativity is contradictory to the time-independent equation of light. Using the time-independent orbital equation to do calculation, the deflection angle of light in the solar gravitational field is 1.75” . But using the time-dependent equation to do calculation, the deflection angle of light is only a small correction of the prediction valve 0.875”of the Newtonian gravity theory with a magnitude order of 10^(-5). The reason causing this inconsistency was the Einstein’s assumption that the motion of light satisfied the condition dS=0in gravitational field. It leads to the absence of constant term in the time-independent equation of motion of light and destroys the uniqueness of geodesic in curved space-time.Meanwhile, light is subject to repulsive forces in the gravitational field, rather then attractive forces. The direction of deflection of light is opposite, inconsistent with the predictions of present general relativity and the Newtonian theory of gravity. Observing on the earth surface, the wavelength of light emitted by the sun is violet shifted. This prediction is obviously not the true. Practical observation is red shift. Finally, the practical significance of the calculation of the Mercury perihelion’s precession and the existing problems of the light’s deflection experiments of general relativity are briefly discussed. The conclusion of this paper is that general relativity can not have consistence with the Newtonian theory of gravity for the descriptions of motions of planets and light in the solar system. The theory itself is not self-consistent too. The Einstein’s gravity theory of curved space-time can not hold.
A Generalized Theory of Gravitation
Reviews of Modern Physics, 1948
' 'N the following we shall give a new presentation of the generalized theory of gravitation, which constitutes a certain progress in clarity as compared to the previous presentations. * It is our aim to achieve a theory of the total field by a generalization of the concepts and methods of the relativistic theory of gravitation. i. THE FIELD STRUCTURE The theory of gravitation represents the field by a symmetric tensor g;~, i.e. , g;q=gq;(i, k=&,~, 4), where the g,t ar e real functions of Xgp ' ' ' X4 In the generalized theory the total field is represented by a Hermitian tensor. The symmetry property of the (complex) g;& is gik gkiĨ f we decompose g,& into its real and imaginary components, then the former is a symmetric tensor (g;&), the latter an antisymmetric tensor (gp). The g;s are still functions of the real variables x~, .~, x4.
About Modelling of the Gravitational Fields
International Journal of Recent advances in Physics, 2015
Within the framework of the general theory of relativity (GR) the modeling of the central symmetrical gravitational field is considered. The mapping of the geodesic motion of the Lemetr and Tolman basis on their motion in the Minkowski space on the world lines is determined. The expression for the field intensity and energy where these bases move is obtained. The advantage coordinate system is found, the coordinates and the time of the system coincide with the Galilean coordinates and the time in the Minkowski space.
A Classical Model of Gravitation
A classical model of gravitation is proposed with time as an independent coordinate. The dynamics of the model is determined by a proposed Lagrangian. Applying the canonical equations of motion to its associated Hamiltonian gives conservation equations of energy, total angular momentum and the z component of the angular momentum. These lead to a Keplerian orbit in three dimensions, which gives the observed values of perihelion precession and bending of light by a massive object. An expression for gravitational redshift is derived by accepting the local validity of special relativity at all points in space. Exact expressions for the GEM relations, as well as their associated Lorentz-type force, are derived. An expression for Mach's Principle is also derived.
A New Approach to General Relativity
Nature, 1961
Here we present a new point of view for general relativity and/or space-time metrics that is remarkably different from the well-known viewpoint of general relativity. From this unique standpoint, we attempt to derive a new metric as an alternative to the Schwarzschild metric for any planet in the solar system. After determining the metric by means of some simple mathematical and physical manipulations, we used this alternative metric to recalculate the perihelion precession of any planet in the solar system and deflection of light that passes near the sun, as examples of this new viewpoint. While we obtained the result of classical general relativity for the perihelion procession, we found a slightly different result, relative to classical general relativity, for the deflection of light.
2008
A new proof of the geodesic character of all motions of bodies that interact only gravitationally - and a detailed illustration of the real meaning of the linearized approximation of general relativity.