The precise calculations of the constant terms in the equations of motions of planets and photons of general relativity

2021 ◽  
Vol 34 (2) ◽  
pp. 183-192
Author(s):  
Mei Xiaochun
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Deflection Angle ◽  
Constant Term ◽  
Equation Of Motion ◽  
Time Dependent ◽  
Newtonian Gravity ◽  
Newtonian Theory ◽  
The Deflection Angle ◽  
Equations Of Motions

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 in this paper that 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 cannot 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 <mml:math display="inline"> <mml:mrow> <mml:mn>1.7</mml:mn> <mml:msup> <mml:mn>5</mml:mn> <mml:mo>″</mml:mo> </mml:msup> </mml:mrow> </mml:math> . But using the time-dependent equation to do calculation, the deflection angle of light is only a small correction of the prediction value <mml:math display="inline"> <mml:mrow> <mml:mn>0.87</mml:mn> <mml:msup> <mml:mn>5</mml:mn> <mml:mo>″</mml:mo> </mml:msup> </mml:mrow> </mml:math> of the Newtonian gravity theory with a magnitude order of <mml:math display="inline"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> . The reason causing this inconsistency was the Einstein's assumption that the motion of light satisfied the condition <mml:math display="inline"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mi>s</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> in 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 subjected to repulsive forces in the gravitational field, rather than 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 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 cannot 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.

scholarly journals Relativity and View Effects

2020 ◽  
Author(s):  
Bernard Fischli
Keyword(s):  
General Relativity ◽  
Deflection Angle ◽  
Point Of View ◽  
Speed Limit ◽  
Implicit Assumption ◽  
Energy Exchanges ◽  
Newton’S Laws ◽  
The Deflection Angle ◽  
New Interpretation ◽  
Relativistic View

Abstract Relativity has been based on the implicit assumption that electromagnetism would exclusively describe interactions. Relativistic view effects are included as well, and they act with no force and no energy exchanges. The Ehrenfest paradox is solved. View effects specific to each point of view are the solution. The calculation of the deflection of light by the sun explains in detail why the deflection angle must be almost double the value obtained with Newton’s laws. The compatibility of General Relativity with the new interpretation is discussed. View effects cannot impact total energy. An object has no speed limit due to relativity but can be limited due to other causes. Inertial behavior is examined. Inertial masses are redundant, but this does not introduce gravitation to General Relativity.

scholarly journals Relativity and View Effects

2020 ◽  
Author(s):  
Bernard Fischli
Keyword(s):  
General Relativity ◽  
Deflection Angle ◽  
Point Of View ◽  
Speed Limit ◽  
Implicit Assumption ◽  
Energy Exchanges ◽  
Newton’S Laws ◽  
The Deflection Angle ◽  
New Interpretation ◽  
Relativistic View

Abstract Relativity has been based on the implicit assumption that electromagnetism would exclusively describe interactions. Relativistic view effects are included as well, and they act with no force and no energy exchanges. The Ehrenfest paradox is solved. View effects specific to each point of view are the solution. The calculation of the deflection of light by the sun explains in detail why the deflection angle must be almost double the value obtained with Newton’s laws. The compatibility of General Relativity with the new interpretation is discussed. View effects cannot impact total energy. An object has no speed limit due to relativity but can be limited due to other causes. Inertial behavior is examined. Inertial masses are redundant, but this does not introduce gravitation to General Relativity.

GRAVITATIONAL FIELD OF A STRAIGHT COSMIC STRING IN THE FRAMEWORK OF HIGHER-DERIVATIVE GRAVITY

2008 ◽  
Vol 23 (24) ◽  
pp. 1999-2009 ◽  
Author(s):  
ANTONIO ACCIOLY ◽  
JOSÉ HELAYËL-NETO ◽  
MATHEUS LOBO
Keyword(s):  
Gravitational Field ◽  
Cosmic String ◽  
Short Range ◽  
Gravitational Force ◽  
Deflection Angle ◽  
Einstein Gravity ◽  
Nonrelativistic Limit ◽  
Higher Derivative ◽  
The Deflection Angle ◽  
The Impact

The gravitational properties of a straight cosmic string are studied in the linear approximation of higher-derivative gravity. These properties are shown to be very different from those found using linearized Einstein gravity: there exists a short range gravitational (anti-gravitational) force in the nonrelativistic limit; in addition, the deflection angle of a light ray moving in a plane orthogonal to the string depends on the impact parameter.

scholarly journals Relativity and View Effects

2020 ◽  
Author(s):  
Bernard Fischli
Keyword(s):  
General Relativity ◽  
Deflection Angle ◽  
Point Of View ◽  
Speed Limit ◽  
Implicit Assumption ◽  
Energy Exchanges ◽  
Newton’S Laws ◽  
The Deflection Angle ◽  
New Interpretation ◽  
Relativistic View

Abstract Relativity has been based on the implicit assumption that electromagnetism would exclusively describe interactions. Relativistic view effects are included as well, and they act with no force and no energy exchanges. The Ehrenfest paradox is solved. View effects specific to each point of view are the solution. The calculation of the deflection of light by the sun explains in detail why the deflection angle must be almost double the value obtained with Newton’s laws. The compatibility of General Relativity with the new interpretation is discussed. View effects cannot impact total energy. An object has no speed limit due to relativity but can be limited due to other causes. Inertial behavior is examined. Inertial masses are redundant, but this does not introduce gravitation to General Relativity.

scholarly journals Hills and holes in the microlensing light curve due to plasma environment around gravitational lens

2019 ◽  
Vol 491 (4) ◽  
pp. 5636-5649 ◽  
Author(s):  
Oleg Yu Tsupko ◽  
Gennady S Bisnovatyi-Kogan
Keyword(s):  
Gravitational Field ◽  
Light Curve ◽  
Significant Influence ◽  
Deflection Angle ◽  
Inhomogeneous Plasma ◽  
Light Curves ◽  
Gravitational Lens ◽  
Remarkable Effect ◽  
The Deflection Angle ◽  
Hole Effect

ABSTRACT In this paper, we investigate the influence of the plasma surrounding the gravitational lens on the effect of microlensing. In presence of plasma around the lens, the deflection angle is determined by both the gravitational field of the lens and the chromatic refraction in the inhomogeneous plasma. We calculate microlensing light curves numerically for point-mass lens surrounded by power-law density distribution of plasma. A variety of possible curves is revealed, depending on the plasma density and frequency of observations. In the case of significant influence of plasma, the shape of microlensing light curve is strongly deformed in comparison with vacuum case. If the refractive deflection is large enough to compensate or to overcome the gravitational deflection, microlensing images can completely disappear for the observer. In this case, the remarkable effect occurs: formation of a ‘hole’ instead of a ‘hill’ in the center of microlensing light curve. Observational prospects of ‘hill-hole’ effect in different microlensing scenarios are discussed.

Relativity and View Effects

2021 ◽  
Author(s):  
Bernard Fischli
Keyword(s):  
General Relativity ◽  
Deflection Angle ◽  
Point Of View ◽  
Speed Limit ◽  
Implicit Assumption ◽  
Energy Exchanges ◽  
Newton’S Laws ◽  
The Deflection Angle ◽  
New Interpretation ◽  
Relativistic View

Abstract Relativity has been based on the implicit assumption that electromagnetism would exclusively describe interactions. Relativistic view effects are included as well, and they act with no force and no energy exchanges. The Ehrenfest paradox is solved. View effects specific to each point of view are the solution. The calculation of the deflection of light by the sun explains in detail why the deflection angle must be almost double the value obtained with Newton’s laws. The compatibility of General Relativity with the new interpretation is discussed. View effects cannot impact total energy. An object has no speed limit due to relativity but can be limited due to other causes. Inertial behavior is examined. Inertial masses are redundant, but this does not introduce gravitation to General Relativity.

The power of weak-field GR gravity

2016 ◽  
Vol 25 (12) ◽  
pp. 1644017 ◽  
Author(s):  
F. I. Cooperstock
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Rotation Curve ◽  
Weak Field ◽  
Gps Tracking ◽  
Galactic Dynamics ◽  
Newtonian Gravity ◽  
Galactic Rotation ◽  
Compatibility Equation ◽  
Galactic Rotation Curve

While general relativity (GR) is our premier theory of gravity, galactic dynamics from the outset has been studied with Newtonian gravity (NG), guided by the long-held belief in the idea of the “Newtonian-limit” of GR. This maintains that when the gravitational field is weak and the velocities are nonrelativistic, NG is the appropriate theory, apart from small corrections at best (such as in GPS tracking). However, there are simple examples of phenomena where there is no NG counterpart. We present a particularly simple new example of the stark difference that NG and weak-field GR exhibit for a modified van Stockum source, which speaks to the flat galactic rotation curve problem. We note that the linear GR compatibility equation in the literature is incomplete. Its completion is vital for our case, leading to a stark contrast between GR and NG for totally flat van Stockum rotation curves.

scholarly journals The Advance of Planets' Perihelion in Newtonian Theory Plus Gravitational and Rotational Time Dilation

2020 ◽  
Author(s):  
Christian Corda
Keyword(s):  
General Relativity ◽  
Body Problem ◽  
Time Dilation ◽  
Newtonian Gravity ◽  
Real Problem ◽  
Newtonian Theory ◽  
Newtonian Physics ◽  
Two Body Problem ◽  
The One ◽  
Very High

It is shown through three different approaches that, contrary to a longstanding conviction older than 160 years, the orbit of Mercury behaves as required by Newton's equations with a very high precision if one correctly analyzes the situation in the framework of the two-body problem without neglecting the mass of Mercury. General relativity remains more precise than Newtonian physics, but the results in this paper show that Newtonian framework is more powerful than researchers and astronomers were thinking till now, at least for the case of Mercury. The Newtonian formula of the advance of planets' perihelion breaks down for the other planets. The predicted Newtonian result is indeed too strong for Venus and Earth. Therefore, it is also shown that corrections due to gravitational and rotational time dilation, in an intermediate framework which analyzes gravity between Newton and Einstein, solve the problem. By adding such corrections, a result consistent with the one of general relativity is indeed obtained. Thus, the most important results of this paper are two: i) It is not correct that Newtonian theory cannot predict the anomalous rate of precession of the perihelion of planets' orbit. The real problem is instead that a pure Newtonian prediction is too strong. ii) Perihelion's precession can be achieved with the same precision of general relativity by extending Newtonian gravity through the inclusion of gravitational and rotational time dilation effects. This second result is in agreement with a couple of recent and interesting papers of Hansen, Hartong and Obers. Differently from such papers, in the present work the importance of rotational time dilation is also highlighted.

scholarly journals Relativity and View Effects

2021 ◽  
Author(s):  
Bernard Fischli
Keyword(s):  
General Relativity ◽  
Deflection Angle ◽  
Point Of View ◽  
Speed Limit ◽  
Implicit Assumption ◽  
Energy Exchanges ◽  
Newton’S Laws ◽  
The Deflection Angle ◽  
New Interpretation ◽  
Relativistic View

Abstract Relativity has been based on the implicit assumption that electromagnetism would exclusively describe interactions. Relativistic view effects are included as well, and they act with no force and no energy exchanges. The Ehrenfest paradox is solved. View effects specific to each point of view are the solution. The calculation of the deflection of light by the sun explains in detail why the deflection angle must be almost double the value obtained with Newton’s laws. The compatibility of General Relativity with the new interpretation is discussed. View effects cannot impact total energy. An object has no speed limit due to relativity but can be limited due to other causes. Inertial behavior is examined. Inertial masses are redundant, but this does not introduce gravitation to General Relativity.

scholarly journals Relativity and View Effects

2020 ◽  
Author(s):  
Bernard Fischli
Keyword(s):  
General Relativity ◽  
Deflection Angle ◽  
Point Of View ◽  
Speed Limit ◽  
Implicit Assumption ◽  
Energy Exchanges ◽  
Newton’S Laws ◽  
The Deflection Angle ◽  
New Interpretation ◽  
Relativistic View

Abstract Relativity has been based on the implicit assumption that electromagnetism would exclusively describe interactions. Relativistic view effects are included as well, and they act with no force and no energy exchanges. The Ehrenfest paradox is solved. View effects specific to each point of view are the solution. The calculation of the deflection of light by the sun explains in detail why the deflection angle must be almost double the value obtained with Newton’s laws. The compatibility of General Relativity with the new interpretation is discussed. View effects cannot impact total energy. An object has no speed limit due to relativity but can be limited due to other causes. Inertial behavior is examined. Inertial masses are redundant, but this does not introduce gravitation to General Relativity.

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