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.

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.

On claims that general relativity differs from Newtonian physics for self-gravitating dusts in the low velocity, weak field limit

2015 ◽  
Vol 24 (08) ◽  
pp. 1550065 ◽  
Author(s):  
David R. Rowland
Keyword(s):  
General Relativity ◽  
Solar System ◽  
Relativistic Effects ◽  
Weak Field ◽  
Newtonian Gravity ◽  
Galactic Rotation ◽  
Low Velocity ◽  
Rotation Curves ◽  
Newtonian Physics ◽  
General Relativistic

Galaxy rotation curves are generally analyzed theoretically using Newtonian physics; however, two groups of authors have claimed that for self-gravitating dusts, general relativity (GR) makes significantly different predictions to Newtonian physics, even in the weak field, low velocity limit. One group has even gone so far as to claim that nonlinear general relativistic effects can explain flat galactic rotation curves without the need for cold dark matter. These claims seem to contradict the well-known fact that the weak field, low velocity, low pressure correspondence limit of GR is Newtonian gravity, as evidenced by solar system tests. Both groups of authors claim that their conclusions do not contradict this fact, with Cooperstock and Tieu arguing that the reason is that for the solar system, we have test particles orbiting a central gravitating body, whereas for a galaxy, each star is both an orbiting body and a contributor to the net gravitational field, and this supposedly makes a difference due to nonlinear general relativistic effects. Given the significance of these claims for analyses of the flat galactic rotation curve problem, this article compares the predictions of GR and Newtonian gravity for three cases of self-gravitating dusts for which the exact general relativistic solutions are known. These investigations reveal that GR and Newtonian gravity are in excellent agreement in the appropriate limits, thus supporting the conventional use of Newtonian physics to analyze galactic rotation curves. These analyses also reveal some sources of error in the referred to works.

scholarly journals Is dark matter fact or fantasy? — Clues from the data

2019 ◽  
Vol 28 (14) ◽  
pp. 1944022 ◽  
Author(s):  
Philip D. Mannheim
Keyword(s):  
Dark Matter ◽  
Gravitational Potential ◽  
Rotation Curve ◽  
Newtonian Gravity ◽  
Galactic Rotation ◽  
Global Effect ◽  
Rotation Curves ◽  
Luminous Matter ◽  
Galactic Rotation Curve ◽  
The Universe

We discuss arguments both in favor of and against dark matter. With the repeated failure of experiment to date to detect dark matter we discuss what could be done instead, and to this end look for clues in the data themselves. We identify various regularities in galactic rotation curve data that correlate the total gravitational potential with luminous matter rather than dark matter. We identify a contribution to galactic rotation curves coming from the rest of the visible universe, and suggest that dark matter is just an attempt to describe this global effect in terms of standard local Newtonian gravity within galaxies. Thus the missing mass is not missing at all — it has been hiding in plain sight all along as the rest of the visible mass in the universe.

scholarly journals Accelerated Frames and Galactic Rotation Curves

2018 ◽  
Author(s):  
Sergio C. Ulhoa ◽  
Fernando 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 article the galactic rotation curve is analyzed as an effect of an accelerated reference frame. This phenomenon is the strongest evidence for the so called dark matter. We show that a non-inertial reference frame could explain the experimental data. We also show that general relativity is not enough to complete explain that which encouraged alternatives paths such as the MOND approach. Considering the effect of dark matter as a realization of accelerated reference frames is a simple but powerful hypothesis.

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.

Galactic rotation curve from the space velocities of selected masers

2011 ◽  
Vol 37 (4) ◽  
pp. 254-266 ◽  
Author(s):  
A. S. Stepanishchev ◽  
V. V. Bobylev
Keyword(s):  
Rotation Curve ◽  
Galactic Rotation ◽  
Galactic Rotation Curve

scholarly journals The Massive Dark Corona Of Our Galaxy

1996 ◽  
Vol 173 ◽  
pp. 175-176
Author(s):  
K.C. Freeman
Keyword(s):  
Rotation Curve ◽  
Spiral Galaxies ◽  
Galactic Center ◽  
Galactic Disk ◽  
Galactic Rotation ◽  
Rotation Curves ◽  
Stellar Component ◽  
The Galaxy ◽  
Galactic Rotation Curve

From their rotation curves, most spiral galaxies appear to have massive dark coronas. The inferred masses of these dark coronas are typically 5 to 10 times the mass of the underlying stellar component. I will review the evidence that our Galaxy also has a dark corona. Our position in the galactic disk makes it difficult to measure the galactic rotation curve beyond about 20 kpc from the galactic center. However it does allow several other indicators of the total galactic mass out to very large distances. It seems clear that the Galaxy does indeed have a massive dark corona. The data indicate that the enclosed mass within radius R increases like M(R) ≈ R(kpc) × 1010M⊙, out to a radius of more than 100 kpc. The total galactic mass is at least 12 × 1011M⊙.

Planetary nebulae and the galactic rotation curve

1983 ◽  
Vol 274 ◽  
pp. L61 ◽  
Author(s):  
S. E. Schneider ◽  
Y. Terzian
Keyword(s):  
Rotation Curve ◽  
Planetary Nebulae ◽  
Galactic Rotation ◽  
Galactic Rotation Curve

scholarly journals The Galactic Rotation Curve to R = 18 Kpc

1980 ◽  
Vol 87 ◽  
pp. 213-220 ◽  
Author(s):  
Leo Blitz ◽  
Michel Fich ◽  
Antony A. Stark
Keyword(s):  
Rotation Curve ◽  
Hii Regions ◽  
Molecular Gas ◽  
Galactic Rotation ◽  
Galactocentric Distance ◽  
The Past ◽  
The Galaxy ◽  
Galactic Rotation Curve ◽  
Sizable Number

The major stumbling block in the determination of a rotation curve beyond the solar circle has been the lack of a suitable set of objects with well defined and independently measured distances and velocities which can be observed to large galactocentric radii. Two things have changed this situation. The first was the realization that essentially all local HII regions have associated molecular material. The second was the acquisition of reliable distances to the stars exciting a sizable number of HII regions at large galactocentric radii (Moffat, FitzGerald, and Jackson 1979). Because the velocity of the associated molecular gas can be measured very accurately by means of radio observations of CO, we have been able to overcome the past difficulties and have measured the rotation curve of the Galaxy to a galactocentric distance of 18 kpc.

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