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

2018 ◽  
Author(s):  
Xiao-Song Wang
Keyword(s):  
General Relativity ◽  
Flow Model ◽  
Weak Field ◽  
Coordinate Systems ◽  
Previous Theory ◽  
Metric Tensor ◽  
Riemannian Spacetime ◽  
Einstein's Equation ◽  
Theory Of Gravitation ◽  
Definition Of

There exist some puzzles and difficulties related to Einstein's theory of general relativity. We generalize our previous theory of gravitation by methods of special relativistic continuum mechanics. In inertial coordinate systems, 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. A generalized Einstein's equation is derived in inertial coordinate systems based on some assumptions. This equation reduces to Einstein's equation in case of weak field in harmonic coordinate systems. In some special non-inertial coordinate systems, a second generalized Einstein's equation is derived based on some assumptions. If the field is weak and the coordinate system is quasi-inertial and harmonic, the second generalized Einstein's equation reduces to Einstein's equation. 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

2018 ◽  
Author(s):  
Xiao-Song Wang
Keyword(s):  
General Relativity ◽  
Mechanical Model ◽  
Flow Model ◽  
Weak Field ◽  
Coordinate Systems ◽  
Previous Theory ◽  
Metric Tensor ◽  
Riemannian Spacetime ◽  
Einstein's Equation ◽  
Definition Of

J. C. Maxwell, B. Riemann and H. Poincaré 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 coordinate systems, 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, a generalized Einstein's equation is derived based on some assumptions. This equation reduces to Einstein's equation in case of weak field in harmonic coordinate systems. In some special non-inertial coordinate systems, a second generalized Einstein's equation is derived based on some assumptions. If the field is weak and the coordinate system is quasi-inertial and harmonic, the second generalized Einstein's equation reduces to Einstein's equation. Thus, this theory also explains all the experiments that support the theory of general relativity. There exists some fundamental 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 ◽  
Flow Model ◽  
Weak Field ◽  
Coordinate Systems ◽  
Previous Theory ◽  
Metric Tensor ◽  
Riemannian Spacetime ◽  
Einstein's Equation ◽  
Definition Of

J. C. Maxwell, B. Riemann and H. Poincaré 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 coordinate systems, 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, a generalized Einstein's equation in inertial systems is derived based on some assumptions. This equation reduces to Einstein's equation in case of weak field in harmonic coordinate systems. In some special non-inertial coordinate systems, a second generalized Einstein's equation is derived based on some assumptions. If the field is weak and the coordinate system is quasi-inertial and harmonic, the second generalized Einstein's equation reduces to Einstein's equation. Thus, this theory may also explains all the experiments which support the theory of general relativity. There exists some fundamental differences between this theory and Einstein's 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 Derivation of Generalized Einstein's Equations of Gravitation in Inertial Systems Based on a Sink Flow Model of Particles

2021 ◽  
Author(s):  
Xiao-Song Wang
Keyword(s):  
Reference Frames ◽  
Flow Model ◽  
Weak Field ◽  
Einstein’S Equations ◽  
Previous Theory ◽  
Metric Tensor ◽  
Einstein's Equations ◽  
Riemannian Spacetime ◽  
Definition Of ◽  
Inertial Systems

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. There exist some differences between this theory and Einstein's theory of general relativity.

scholarly journals Universality of the Einstein theory of gravitation

2016 ◽  
Vol 13 (08) ◽  
pp. 1640008 ◽  
Author(s):  
Jerzy Kijowski
Keyword(s):  
General Relativity ◽  
Variational Problems ◽  
Relativity Theory ◽  
General Relativity Theory ◽  
Einstein Theory ◽  
Metric Tensor ◽  
New Approach ◽  
Theory Of Gravitation ◽  
Tensor Formula ◽  
Matter Fields

We show that generalizations of general relativity theory, which consist in replacing the Hilbert Lagrangian [Formula: see text] by a generic scalar density [Formula: see text] depending upon the metric [Formula: see text] and the curvature tensor [Formula: see text], are equivalent to the conventional Einstein theory for a (possibly) different metric tensor [Formula: see text] and (possibly) a different set of matter fields. The simple proof of this theorem relies on a new approach to variational problems containing metric and connection.

scholarly journals A geometric relativistic dynamics under any conservative force

2019 ◽  
Vol 16 (01) ◽  
pp. 1950015 ◽  
Author(s):  
Yaakov Friedman ◽  
Tzvi Scarr ◽  
Joseph Steiner
Keyword(s):  
General Relativity ◽  
Force Field ◽  
Geometric Theory ◽  
Weak Field ◽  
Inanimate Object ◽  
Relativistic Dynamics ◽  
Low Velocity ◽  
Tests Of General Relativity ◽  
Newtonian Dynamics ◽  
Theory Of Gravitation

Riemann’s principle “force equals geometry” provided the basis for Einstein’s General Relativity — the geometric theory of gravitation. In this paper, we follow this principle to derive the dynamics for any static, conservative force. The geometry of spacetime of a moving object is described by a metric obtained from the potential of the force field acting on it. We introduce a generalization of Newton’s First Law — the Generalized Principle of Inertia stating that: An inanimate object moves inertially, that is, with constant velocity, in its own spacetime whose geometry is determined by the forces affecting it. Classical Newtonian dynamics is treated within this framework, using a properly defined Newtonian metric with respect to an inertial lab frame. We reveal a physical deficiency of this metric (responsible for the inability of Newtonian dynamics to account for relativistic behavior), and remove it. The dynamics defined by the corrected Newtonian metric leads to a new Relativistic Newtonian Dynamics for both massive objects and massless particles moving in any static, conservative force field, not necessarily gravitational. This dynamics reduces in the weak field, low velocity limit to classical Newtonian dynamics and also exactly reproduces the classical tests of General Relativity, as well as the post-Keplerian precession of binaries.

scholarly journals Models of Compact Stars in the Bimetric Scalar-Tensor Theory of Gravitation

Particles ◽  
2018 ◽  
Vol 1 (1) ◽  
pp. 203-211 ◽  
Author(s):  
Levon Grigorian ◽  
Hrant Khachatryan ◽  
Aram Saharian
Keyword(s):  
General Relativity ◽  
Scalar Field ◽  
Coupling Function ◽  
Compact Stars ◽  
Spherically Symmetric ◽  
Scalar Tensor Theory ◽  
Metric Tensor ◽  
Tensor Theory ◽  
Theory Of Gravitation ◽  
The Masses

We investigate static spherically-symmetric configurations of gravitating masses in the bimetric scalar-tensor theory of gravitation. In the gravitational sector, the theory contains the metric tensor, a scalar field and a background metric as an absolute variable of the theory. The analysis is presented for the simplest version of the theory with a constant coupling function and a zero cosmological function. We show that, depending on the value of the theory parameter, the masses for superdense compact configurations can be essentially larger compared to the configurations in general relativity.

NEW CLASS OF METRIC THEORIES OF GRAVITY NOT DESCRIBED BY THE PARAMETRIZED POST-NEWTONIAN (PPN) FORMALISM

1991 ◽  
Vol 06 (30) ◽  
pp. 5511-5532 ◽  
Author(s):  
IGNAZIO CIUFOLINI
Keyword(s):  
General Relativity ◽  
A Priori ◽  
Relativistic Effects ◽  
Weak Field ◽  
Metric Tensor ◽  
New Class ◽  
Theories Of Gravity ◽  
Experimental Values ◽  
Ppn Parameters ◽  
Infinite Set

After an introduction to theories of gravity alternative to general relativity, metric theories (Sec. 1) and the parametrized post-Newtonian (PPN) formalism (Sec. 2), we define a new class of metric theories of gravity (Sec. 3). It turns out that the post-Newtonian approximation of these new theories is not described by the PPN formalism (Sec. 4); in fact, in the limit of weak field and slow motions, the post-Newtonian expression of the metric tensor contains an, a priori, infinite set of new terms and correspondingly an, a priori, infinite set of new PPN parameters. As a consequence, the parametrized post-Newtonian formulas describing the classical relativistic tests should include these new parameters, and therefore the experimental values of the classical relativistic effects should not be used to put limits only on the standard ten PPN parameters. Finally, we note that a subset of this new class of theories has the same post-Newtonian limit and value of the PPN parameters as general relativity, and therefore is automatically in agreement with the classical general-relativistic tests (Sec. 4, theory III).

2.2. Working Group 2: Conceptual Definitions of Reference Coordinate Systems for Earth Dynamics

1975 ◽  
Vol 26 ◽  
pp. 21-26
Keyword(s):  
Coordinate System ◽  
Working Group ◽  
General Character ◽  
Coordinate Systems ◽  
Reference Coordinate System ◽  
Group 2 ◽  
Definition Of ◽  
Earth Dynamics

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.

Sign in / Sign up

Export Citation Format

Share Document