scholarly journals Derivation of Generalized Einstein's Equations of Gravitation in Some Non-Inertial Reference Frames Based on the Theory of Vacuum Mechanics

2021 ◽  
Author(s):  
Xiao-Song Wang
Keyword(s):  
General Relativity ◽  
Reference Frame ◽  
Lorentz Transformation ◽  
Special Class ◽  
Wave Equations ◽  
Reference Frames ◽  
Lorentz Transformations ◽  
Einstein’S Equations ◽  
Einstein's Equations

When solving the Einstein's equations for an isolated system of masses, V. Fock introduces harmonic reference frame and obtains an unambiguous solution. Further, he concludes that there exists a harmonic reference frame which is determined uniquely apart from a Lorentz transformation if suitable supplementary conditions are imposed. It is known that wave equations keep the same form under Lorentz transformations. Thus, we speculate that Fock's special harmonic reference frames may have provided us a clue to derive the Einstein's equations in some special class of non-inertial reference frames. Following this clue, generalized Einstein's equations in some special non-inertial reference frames are derived based on the theory of vacuum mechanics. If the field is weak and the reference frame is quasi-inertial, these generalized Einstein's equations reduce to Einstein's equations. Thus, this theory may also explain all the experiments which support the theory of general relativity. There exist some differences between this theory and the theory of general relativity.

Derivation of Generalized Einstein's Equations of Gravitation Based on a Mechanical Model of Vacuum and a Sink Flow Model of Particles

2019 ◽  
Author(s):  
Xiao-Song Wang
Keyword(s):  
General Relativity ◽  
Mechanical Model ◽  
Reference Frames ◽  
Flow Model ◽  
Weak Field ◽  
Einstein’S Equations ◽  
Previous Theory ◽  
Metric Tensor ◽  
Einstein's Equations ◽  
Definition Of

J. C. Maxwell, B. Riemann and H. Poincar$\acute{e}$ have proposed the idea that all microscopic particles are sink flows in a fluidic aether. Following this research program, a previous theory of gravitation based on a mechanical model of vacuum and a sink flow model of particles is generalized by methods of special relativistic continuum mechanics. In inertial reference frames, we construct a tensorial potential which satisfies the wave equation. Inspired by the equation of motion of a test particle, a definition of a metric tensor of a Riemannian spacetime is introduced. Applying Fock's theorem, generalized Einstein's equations in inertial systems are derived based on some assumptions. These equations reduce to Einstein's equations in case of weak field in harmonic reference frames. In some special non-inertial reference frames, generalized Einstein's equations are derived based on some assumptions. If the field is weak and the reference frame is quasi-inertial, these generalized Einstein's equations reduce to Einstein's equations. Thus, this theory may also explains all the experiments which support the theory of general relativity. There exists some differences between this theory and Einstein's theory of general relativity.

scholarly journals Derivation of Generalized Einstein's Equations of Gravitation Based on a Mechanical Model of Vacuum and a Sink Flow Model of Particles

2019 ◽  
Author(s):  
Xiao-Song Wang
Keyword(s):  
General Relativity ◽  
Mechanical Model ◽  
Reference Frames ◽  
Flow Model ◽  
Weak Field ◽  
Einstein’S Equations ◽  
Previous Theory ◽  
Metric Tensor ◽  
Einstein's Equations ◽  
Definition Of

J. C. Maxwell, B. Riemann and H. Poincar$\acute{e}$ have proposed the idea that all microscopic particles are sink flows in a fluidic aether. Following this research program, a previous theory of gravitation based on a mechanical model of vacuum and a sink flow model of particles is generalized by methods of special relativistic continuum mechanics. In inertial reference frames, we construct a tensorial potential which satisfies the wave equation. Inspired by the equation of motion of a test particle, a definition of a metric tensor of a Riemannian spacetime is introduced. Applying Fock's theorem, generalized Einstein's equations in inertial systems are derived based on some assumptions. These equations reduce to Einstein's equations in case of weak field in harmonic reference frames. In some special non-inertial reference frames, generalized Einstein's equations are derived based on some assumptions. If the field is weak and the reference frame is quasi-inertial, these generalized Einstein's equations reduce to Einstein's equations. Thus, this theory may also explains all the experiments which support the theory of general relativity. There exists some differences between this theory and Einstein's theory of general relativity.

scholarly journals Gravity as entanglement, entanglement as gravity

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Reference Frame ◽  
Common Sense ◽  
Reference Frames ◽  
General Covariance ◽  
The Universe

A generalized and unifying viewpoint to both general relativity and quantum mechanics and information is investigated. It may be described as a generaliztion of the concept of reference frame from mechanics to thermodynamics, or from a reference frame linked to an element of a system, and thus, within it, to another reference frame linked to the whole of the system or to any of other similar systems, and thus, out of it. Furthermore, the former is the viewpoint of general relativity, the latter is that of quantum mechanics and information.Ciclicity in the manner of Nicolas Cusanus (Nicolas of Cusa) is complemented as a fundamental and definitive property of any totality, e.g. physically, that of the universe. It has to contain its externality within it somehow being namely the totality. This implies a seemingly paradoxical (in fact, only to common sense rather logically and mathematically) viewpoint for the universe to be repesented within it as each one quant of action according to the fundamental Planck constant.That approach implies the unification of gravity and entanglement correspondiing to the former or latter class of reference frames. An invariance, more general than Einstein's general covariance is to be involved as to both classes of reference frames unifying them. Its essence is the unification of the discrete and cotnitinuous (smooth). That idea underlies implicitly quantum mechanics for Bohr's principle that it study the system of quantum microscopic entities and the macroscopic apparatus desribed uniformly by the smmoth equations of classical physics.e

Physics as an Art Form

2018 ◽  
pp. 1-4
Author(s):  
Alvaro De Rújula
Keyword(s):  
General Relativity ◽  
Laws Of Nature ◽  
Space Time ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
Ockham’S Razor ◽  
Art Form ◽  
Ockham's Razor ◽  
The Universe ◽  
The Way

Beauty and simplicity, a scientist’s view. A first encounter with Einstein’s equations of General Relativity, space-time, and Gravity. Ockham’s Razor. Why the Universe is the way it is: The origin of the laws of Nature.

Accelerated frames and galactic rotation curves

2019 ◽  
Vol 34 (27) ◽  
pp. 1950218
Author(s):  
S. C. Ulhoa ◽  
F. L. Carneiro
Keyword(s):  
Experimental Data ◽  
General Relativity ◽  
Dark Matter ◽  
Reference Frame ◽  
Rotation Curve ◽  
Reference Frames ◽  
Galactic Rotation ◽  
Inertial Reference Frame ◽  
Galactic Rotation Curve ◽  
Accelerated Frames

In this paper, the galactic rotation curve is analyzed as an effect of an accelerated reference frame. Such a rotation curve was the first evidence for the so-called dark matter. We show another possibility for this experimental data: non-inertial reference frame can fit the experimental curve. We also show that general relativity is not enough to completely explain that which encouraged alternatives paths such as the MOND approach. The accelerated reference frames hypothesis is well-suited to deal with the rotation curve of galaxies and perhaps has some role to play concerning other evidences for dark matter.

scholarly journals ON THE ENERGY–MOMENTUM FLUX IN GÖDEL-TYPE MODELS

2013 ◽  
Vol 28 (10) ◽  
pp. 1350039 ◽  
Author(s):  
S. C. ULHOA ◽  
A. F. SANTOS ◽  
R. G. G. AMORIM
Keyword(s):  
General Relativity ◽  
Total Pressure ◽  
Momentum Flux ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
Cartesian Coordinates ◽  
Stationary Observer

In this paper, we work in the context of Teleparallelism Equivalent to General Relativity (TEGR) in order to construct the energy–momentum flux for Gödel-type solutions of Einstein's equations. We use an stationary observer, which is settled by the tetrad choice, to obtain the gravitational pressure for each direction of space in cartesian coordinates. Then, we write down the total pressure for each direction in terms of the pressure of the fluid, thus we are able to identify the role of the gravitational pressure.

Cylindrically symmetric relativistic fluids and the purely electric Weyl tensor

2015 ◽  
Vol 12 (10) ◽  
pp. 1550103 ◽  
Author(s):  
Rajesh Kumar ◽  
S. K. Srivastava ◽  
V. C. Srivastava
Keyword(s):  
General Relativity ◽  
Energy Density ◽  
Weyl Tensor ◽  
Einstein’S Equations ◽  
Relativistic Fluids ◽  
Einstein's Equations ◽  
Cylindrically Symmetric ◽  
Expansion Scalar

In General Relativity (GR), the analysis of electric and magnetic Weyl tensors has been studied by various authors. The present study deals with cylindrically symmetric relativistic fluids in GR characterized by the vanishing of magnetic Weyl tensor-purely electric (PE) fields. A very new assumption has been adapted to solve the Einstein's equations and the obtained solution is shearing at all. We signified the importance of PE fields in the context of expansion scalar, energy density, shear and acceleration.

Some spherical gravitational waves in general relativity

1962 ◽  
Vol 265 (1323) ◽  
pp. 463-473 ◽  
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Empty Space ◽  
Einstein Equations ◽  
Einstein’S Equations ◽  
Killing Field ◽  
Einstein's Equations ◽  
Outgoing Radiation ◽  
Null Curves

Einstein's equations for empty space are solved for the class of metrics which admit a family of hypersurface-orthogonal, non-shearing, diverging null curves. Some of these metrics may be considered as representing a simple kind of spherical, outgoing radiation. (Among them are solutions admitting no Killing field whatsoever.) Examples of solutions to the Maxwell-Einstein equations with a similar geometry are also given.

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