On Maxwell Equations for Gravitational Field

For explicitly time depending mass density which satisfies a continuity equation, it is shown that Maxwell-like equations for gravitational field follow naturally without any need of General Relativity Theory approximation or related assumptions. As a consequence, it is shown that several features already known in Electrodynamics (Poynting vector, density of energy, tensor stress, and radiation) are totally reproduced for gravitational field.

Bach-Einstein Gravitational Field Equations as a Perturbation of Einstein Gravitational Field Equations

The Bach equations are a version of higher-order gravitational field equations, exactly they are of fourth-order. In 4-dimensions the Bach-Einstein gravitational field equations are treated here as a perturbation of Einstein’s gravity. An approximate inversion formula is derived which admits a comparison of the two field theories. An application to these theories is given where the gravitational Lagrangian is expressed linearly in terms of R, R2, |Ric|2, where the Ricci tensor Ric = Rαβdxαdxβ is inserted in some formulas which are of geometrical or physical importance, such as;Raychaudhuri equation and Tolman’s formula.

Pulsation Solution to the Equation of Earth's Gravitational Field (Main Outcome)

Using d'Alembert equation as the approximation of Einstein's equation, a solution is given in this paper to the time-dependent gravitational equation of the Earth in consideration of the Earth's features, which describes the characteristics of pulsation of the Earth and the structures of spherical layers of its interior, thus providing a theoretical basis for establishing the idea of mantle pulsation.

The Maxwell-Heaviside Equations Explained by the Theory of Informatons

In the articles “Newtons Law of Universal Gravitation Explained by the Theory of Informatons” and “The Gravitational Interaction between Moving Mass Particles Explained by the Theory of Informatons” the gravitational interaction has been explained by the hypothesis that information carried by informatons is the substance of gravitational fields, i.e. the medium that the interaction in question makes possible. From the idea that “information carried by informatons” is its substance, it has been deduced that—on the macroscopic level—a gravitational field manifests itself as a dual entity, always having a field- and an induction component (Egand Bg) simultaneously created by their common sources. In this article we will mathematically deduce the Maxwell-Heaviside equations from the kinematics of the informatons. These relations describe on the macroscopic level how a gravitational field (Eg, Bg) is generated by whether or not moving masses and how spatial and temporal changes of Egand Bgare related. We show that there is no causal link between Egand Bg.

Unified Field Equation Generated by Longitudinal Electromagnetic (LEM) Waves

According to special relativity,the relationship of electromagnetic conversion in a linear moving vacuum and the relationship formula between the magnetic vector potential/scalar potential and the LEM(Longitudinal Electromagnetic)waves,it is inferred that the spherical vacuum space we are in undergoes outward helical motion at the speed of light following the right-hand screw rule,accompanied by a radial space expansion motion far less than the speed of light.Based on this space basis,we derive a unified field equation indicating that the gravitational field might be equivalent to the acceleration field of the radial expansion motion of our vacuum space,the strong nuclear force field presumably is generated by the light-rotation angular velocity of our space,the weak nuclear force field is most probably produced by its radial expansion motion and the electromagnetic field is undoubtedly produced by the radial linear motion of our space at the speed of light.We have also demonstrated both theoretically and experimentally that the LEM waves can generate artificial gravitational fields,and the LEM waves are the material basis of the unified field theory.Essentially,on Earth,time is the result of the relativistic length contraction effect caused by the radial space expansion speed,which leads to the rate of change of distance in the radial dimension on the unit radial space expansion speed.Moreover,based on the length contraction effect in special relativity,the time and space generated by the outward helical motion of space at the speed of light can be expressed as zero.This indicates that such motion not only does not affect the seemingly perpetually stationary space that we can constantly perceive but also enables the gravitational field formula to remain unchanged in our space.They constitute the spatio-temporal basis of the unified field theory.Based on our unified field theory,we have also discussed some forward-looking perspectives,such as motion at the speed of light,anti-gravitation fields,and interstellar travel.

The Singularities of Gravitational Fields of Static Thin Loop and Double Spheres Reveal the Impossibility of Singularity Black Holes

In the classical Newtonian mechanics, the gravity fields of static thin loop and double spheres are two simple but foundational problems. However, in the Einstein’s theory of gravity, they are not simple. In fact, we do not know their solutions up to now. Based on the coordinate transformations of the Kerr and the Kerr-Newman solutions of the Einstein’s equation of gravity field with axial symmetry, the gravity fields of static thin loop and double spheres are obtained. The results indicate that, no matter how much the mass and density are, there are singularities at the central point of thin loop and the contact point of double spheres. What is more, the singularities are completely exposed in vacuum. Space near the surfaces of thin loop and spheres are highly curved, although the gravity fields are very weak. These results are inconsistent with practical experience and completely impossible. By reasonable analogy, black holes with singularity in cosmology and astrophysics are something illusive. Caused by the mathematical description of curved space-time, they do not exist in real world actually. If there are black holes in the universe, they can only be the types of the Newtonian black holes without singularities, rather than the Einstein’s singularity black holes. In order to escape the puzzle of singularity thoroughly, the description of gravity should return to the traditional form of dynamics in flat space. The renormalization of gravity and the unified description of four basic interactions may be possible only based on the frame of flat space-time. Otherwise, theses problems can not be solved forever. Physicists should have a clear understanding about this problem.

How Classical, Quantum-Mechanical, and Relativistic Wave and Field Equations Are Uniformly Generated by Velocity-Field Divergence Equations

We expand previously established results concerning the uniform representability of classical and relativistic gravitational field equations by means of velocity-field divergence equations by demonstrating that conservation equations for (probability) density functions give rise to velocity-field divergence equations the solutions of which generate—by way of superposition—the totality of solutions of various well-known classical and quantum-mechanical wave equations.

A CALCULATION METHOD TO THE PERTURBATION OF A SATELLITE CAUSED BY THE GRAVITATION FIELD OF THE EARTH

In this paper, with the application of the Delauney variables, according to the Hamilton equations, the influence on the perturbation of a satellite exerted by the gravitational force of the earth through canonical transformation has been found out. As a result, the equation about how the position and velocity of the satellite vary with time is deduced.

On Quasi-Einstein Field Equation

In this paper some properties of a symmetric tensor field T（X,Y） = g（A（X）, Y） on a Riemannian manifold （M, g） without boundary which satisfies the S quasi-Einstein equation Rij-S/2gij=Tij＋bξiξj are given. The necessary and sufficient conditions for this tensor to satisfy the quasi-Einstein equation are also obtained.

Newtonian Gravitational Radiation and Waves

In this paper, we review historical Maxwell's equation for gravity and recent studies on the lack of curvature of linear dipole gravitational waves. The extended Newton's gravity necessarily has the continuity equation for the conservation of mass, and with the Gauss' equation associated to gravitational time depending field R, bring about a new field W which resembles the magnetic field in Electrodynamics. Although this field has not been found yet, its existence comes from a strong mathematical statement, and it is shown that linear dipole gravitational waves have their origin in extended Newton theory of gravity. This is a direct mathematical consequence of Gauss' law and the continuity equation for the density of mass and current, and as a direct result of this, any accelerated mass will emit mainly dipole gravitational radiation. Then, one concludes that dipole gravitational waves can have its origin on the extended Newton's gravity equations.

Gravitational Space-Time Curve Generation via Accelerated Charged Particles

A force with an acceleration that is equal to multiples greater than the speed of light per unit time is exerted on a cloud of charged particles. The particles are resultantly accelerated to within an infinitesimal fraction of the speed of light. As the force or acceleration increases, the particles’ velocity asymptotically approaches but never achieves the speed of light obeying relativity. The asymptotic increase in the particles’ velocity toward the speed of light as acceleration increasingly surpasses the speed of light per unit time does not compensate for the momentum value produced on the particles at sub-light velocities. Hence, the particles’ inertial mass value must increase as acceleration increases. This increase in the particles’ inertial mass as the particles are accelerated produce a gravitational field which is believed to occur in the oscillation of quarks achieving velocities close to the speed of light. The increased inertial mass of the density of accelerated charged particles becomes the source mass (or Big “M”) in Newton’s equation for gravitational force. This implies that a space-time curve is generated by the accelerated particles. Thus, it is shown that the acceleration number (or multiple of the speed of light greater than 1 per unit of time) and the number of charged particles in the cloud density are surjectively mapped to points on a differential manifold or space-time curved surface. Two aspects of Einstein’s field equations are used to describe the correspondence between the gravitational field produced by the accelerated particles and the resultant space-time curve. The two aspects are the Schwarzchild metric and the stress energy tensor. Lastly, the possibility of producing a sufficient acceleration or electromagnetic force on the charged particles to produce a gravitational field is shown through the Lorentz force equation. Moreover, it is shown that a sufficient voltage can be generated to produce an acceleration/force on the particles that is multiples greater than the speed of light per unit time thereby generating gravity.

A Self-Stabilized Field Theory of Neutrinos

In “A Self-linking Field Formalism” I establish a self-dual field structure with higher order self-induced symmetries that reinforce the first-order dynamics. The structure was derived from Gauss-linking integrals in R3 based on the Biot-Savart law and Ampere’s law applied to Heaviside’s equations, derived in strength-independent fashion in “Primordial Principle of Self-Interaction”. The derivation involves Geometric Calculus, topology, and field equations. My goal in this paper is to derive the simplest solution of a self-stabilized solitonic structure and discuss this model of a neutrino.

Maxwell-Proca Fields in Relativistic Astrophysical Compact Objects

A general-relativistic model is formulated for hypothetical ultra-compact astrophysical objects composed of fluid infused with charges carrying a generalized massless Maxwell-Proca field. The chosen interior metric has the algebraic property that;the fluid consequently possesses a negative pressure which halts gravitational collapse and establishes hydrostatic equilibrium. For an object containing a global distribution of non-interacting Maxwell-Proca charges, it is shown that physical considerations define the relationship between the charge density and the metric function uniquely, corroborating an earlier finding (for an electrostatic distribution of charge) that the interior field must increase with radial distance and the exterior field necessarily follows an inverse-square law. For the case of a charged fluid envelope surrounding a core of uncharged fluid, numerous solutions are possible. Assuming the interior field to vary as rn and requiring its strength to increase with radial distance while the charge density decreases, the range of values for n is found to be 0 n ≤ 1 (where n is not necessarily an integer) with n = 1 denoting the special case of a continuous distribution of charge. For both continuous and stratified charge distributions, the exterior field is found to decrease as 1/r2?regardless of the interior field’s dependence on r.

Origin of Magnetic Fields of Stellar Objects in the Universe Based on the 5D Projection Theory

Beginning with a 5D homogeneous universe [1], we have provided a plausible explanation of the self-rotation phenomenon of stellar objects previously with illustration of large number of star samples [2], via a 5D-4D projection. The origin of such rotation is the balance of the angular momenta of stars and that of positive and negative charged e-trino pairs, within a 3D ⊗1D?void of the stellar object, the existence of which is based on conservation/parity laws in physics if one starts with homogeneous 5D universe. While the in-phase e-trino pairs are proposed to be responsible for the generation of angular momentum, the anti-phase but oppositely charge pairs necessarily produce currents. In the 5D to 4D projection, one space variable in the 5D manifold was compacted to zero in most other 5D theories (including theories of Kaluza-Klein and Einstein [3] [4]). We have demonstrated, using the Fermat’s Last Theorem [5], that for validity of gauge invariance at the 4D-5D boundary, the 4th space variable in the 5D manifold is mapped into two current rings at both magnetic poles as required by Perelman entropy mapping;these loops are the origin of the dipolar magnetic field. One conclusion we draw is that there is no gravitational singularity, and hence no black holes in the universe, a result strongly supported by the recent discovery of many stars with masses well greater than 100 solar mass [6] [7] [8], without trace of phenomena observed (such as strong gamma and X ray emissions), which are supposed to be associated with black holes. We analyze the properties of such loop currents on the 4D-5D boundary, where Maxwell equations are valid. We derive explicit expressions for the dipolar fields over the whole temperature range. We then compare our prediction with measured surface magnetic fields of many stars. Since there is coupling in distribution between the in-phase and anti-phase pairs of e-trinos, the generated mag-netic field is directly related to the angular momentum, leading to the result that the magnetic field can be expressible in terms of only the mechanical variables (mass M, radius R, rotation period P)of a star, as if Maxwell equations are “hidden”. An explanation for the occurrence of this “un-expected result” is provided in Section (7.6). Therefore we provide satisfactory answers to a number of “mysteries” of magnetism in astrophysics such as the “Magnetic Bode’s Relation/Law” [9] and the experimental finding that B-P graph in the log-log plot is linear. Moreover, we have developed a new method for studying the relations among the data (M, R, P) during stellar evolution. Ten groups of stellar objects, effectively over 2000 samples are used in various parts of the analysis. We also explain the emergence of huge magnetic field in very old stars like White Dwarfs in terms of formation of 2D Semion state on stellar surface and release of magnetic flux as magnetic storms upon changing the 2D state back to 3D structure. Moreover, we provide an explanation, on the ground of the 5D theory, for the detection of extremely weak fields in Venus and Mars and the asymmetric distribution of magnetic field on the Martian surface. We predict the equatorial fields B of the newly discovered Trappist-1 star and the 6 nearest planets. The log B?−?log P graph for the 6 planets is linear and they satisfy the Magnetic Bode’s relation. Based on the above analysis, we have discovered several new laws of stellar magnetism, which are summarized in Section (7.6).

On the Transition from Newtonian Gravity to General Relativity

Using an alternative representation of the Ricci tensor, we argue that the theory of gravitation can be easily developed in such a way that the formal description of gravity in the transition from classical Newtonian physics to general relativity remains essentially unchanged. That is to say, we show how arguments concerning the plausible conceptual compatibility of Newtonian and general-relativistic models of gravity can be replaced by a demonstration of their actual formal identity. More specifically, we find that both the classical Newtonian and the general relativistic field equations are equivalent to a velocity-field divergence equation of the form v [div (v)] + div (v,v) = -4πρ where the term div (v,v) is defined to be the trace of the square of the Jacobian derivative matrix of v (or of its general-relativistic analogue).

On the Quantization of Time, Space and Gravity

We combine the de Broglie Matter Wave Equation with the Heisenberg Uncertainty Principle to derive an equation for time as a wave. This happens to be the first time that these two statements have been combined in this manner to derive an equation for time. The result is astounding. Time turns out to be a minuscule blob of quantum electromagnetic energy in perpetual angular momentum. From this time equation, we derive an equation for space which turns out to also predict a string (like the string of string theory). We then combine the time equation with the space equation to derive an equation for the inverse of quantum gravity which is also surprisingly electromagnetic in nature. This last statement implies that space is multidimensional and gravity in multidimensional space is not quantized, but its inverse (which is single-dimensional) is.

Higher Order Self-Induced Self-Interacting Field

The genesis of physical particles is essentially a mystery. Quantum field theory creation operators provide an abstract mechanism by which particles come into existence, but quantum fields do not possess energy density. I reference several recent treatments of this problem and develop ideas based on self-stabilizing field structures with focus on higher order self-induced self-stabilizing field structures. I extend this treatment in this paper to related issues of topological charge.

在重力场中的热力学基本方程及应用

通过引入组分B的摩尔重力势能,导出了在重力场中多组分系统的热力学基本方程。定义了重力化学势,据此判断变化的方向和限度。最后列举了重力化学势判据的应用实例:理想气体压力随高度分布公式,溶胶粒子在介质中沉降平衡公式。

Analysis of the Electromagnetic Characteristics and the Mechanism Underlying Bio-Medical Function of Longitudinal Electromagnetic (LEM) Waves

Based on theoretical system of current Maxwell’s equations, the Maxwell’s equations for LEM waves concealed in full current law and Faraday’s law of electromagnetic induction (Faraday’s law) are proposed. Then, taking them as the fundamental equations, the wave equation and energy equation of LEM waves are established, and a new electromagnetic wave propagation mode based on the mutual induction of scalar electromagnetic fields/vortex magneto-electric fields, which was overlooked in current Maxwell’s equations, are put forward. Moreover, through theoretical derivation based on vacuum LEM waves, the Maxwell’s equations of the gravitational field generated by vacuum LEM waves, the wave equations of the electromagnetic scalar potential/magnetic vector potential and the constraint equation governing the wave phase-velocities between LEM/TEM waves are discovered. Finally, on the basis of these theoretical research results, the electromagnetic properties of vacuum LEM waves are analyzed in detail, encompassing the speed of light, harmless penetrability to the human body, absorption and stable storage by water, the possibility of generating artificial gravitational fields, and the capability of extracting free energy. This reveals the medical functional mechanism of LEM waves and establishes a solid theoretical basis for the application of LEM waves in the fields of medicine and energy.

ASYMPTOTICALLY FLAT GRAVITATIONAL FIELD OF A REALISTIC MONOPOLE OR DYON

Ⅰ. INTRODUCTION As is well-known, topological defects of various types may have been created by vacuum phase transitions in the early universe. The type of defects depends on the topology of vacuum manifold. In particular, monopoles are formed when the homotopy group π2 （G/H）is nontrivial. The monopoles formed as a result of a gauge symmetry breaking are similar to ele-