scholarly journals Excluded Volume for Flat Galaxy Rotation Curves in Newtonian Gravity and General Relativity

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 398 ◽  
Author(s):  
Rand Dannenberg
Keyword(s):  
General Relativity ◽  
Gravitational Constant ◽  
Excluded Volume ◽  
Newtonian Gravity ◽  
Least Action Principle ◽  
Rotation Curves ◽  
Least Action ◽  
A Charge ◽  
Vacuum Solutions ◽  
Galaxy Rotation Curves

Using the classical vacuum solutions of Newtonian gravity that do not explicitly involve matter, dark matter, or the gravitational constant, subject to an averaging process, a form of gravity relevant to the flattening of galaxy rotation curves results. The latter resembles the solution found if the vacuum is simply assigned a gravitational field density, and a volume of the vacuum is then excluded, with no averaging process. A rationale then follows for why these terms would become important on the galactic scale. Then, a modification of General Relativity, motivated by the Newtonian solutions, that are equivalent to a charge void, is partially defined and discussed in terms of a least action principle.

scholarly journals On galaxy rotation curves from a continuum mechanics approach to modified gravity

2018 ◽  
Vol 27 (02) ◽  
pp. 1850007 ◽  
Author(s):  
Christian G. Böhmer ◽  
Nicola Tamanini ◽  
Matthew Wright
Keyword(s):  
General Relativity ◽  
Dark Matter ◽  
Continuum Mechanics ◽  
Modified Gravity ◽  
Galactic Rotation ◽  
Dark Matter Halos ◽  
Additional Structure ◽  
Rotation Curves ◽  
Small Deviations ◽  
Galaxy Rotation Curves

We consider a modification of General Relativity motivated by the treatment of anisotropies in Continuum Mechanics. The Newtonian limit of the theory is formulated and applied to galactic rotation curves. By assuming that the additional structure of spacetime behaves like a Newtonian gravitational potential for small deviations from isotropy, we are able to recover the Navarro–Frenk–White profile of dark matter halos by a suitable identification of constants. We consider the Burkert profile in the context of our model and also discuss rotation curves more generally.

QUANTUM MECHANICS FROM A FLUCTUATION IN THE COSMOS

2001 ◽  
Vol 16 (17) ◽  
pp. 2965-2973 ◽  
Author(s):  
MAKOTO INABA
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Scalar Curvature ◽  
Mass Distribution ◽  
Coarse Graining ◽  
Present Theory ◽  
Random Motion ◽  
Least Action Principle ◽  
Least Action ◽  
The Universe

There is an indeterminable part from only the mass distribution in the general relativity. The part is regarded as a fluctuation from the Robertson–Walker geometry. An ensemble is given by a coarse graining of the fluctuation. The averaged least-action principle with respect to the ensemble yields a random motion of a particle in the universe. The random motion is equivalent to the traditional quantum mechanics. There is an additional potential proportional to scalar curvature in the present theory. The potential may be a representation of Mach's principle.

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 A least action principle for interceptive walking

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Soon Ho Kim ◽  
Jong Won Kim ◽  
Hyun Chae Chung ◽  
MooYoung Choi
Keyword(s):  
Social Systems ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Action Principle ◽  
Lagrange Equations ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle ◽  
Principle Of Least Action ◽  
Human Participants

AbstractThe principle of least effort has been widely used to explain phenomena related to human behavior ranging from topics in language to those in social systems. It has precedence in the principle of least action from the Lagrangian formulation of classical mechanics. In this study, we present a model for interceptive human walking based on the least action principle. Taking inspiration from Lagrangian mechanics, a Lagrangian is defined as effort minus security, with two different specific mathematical forms. The resulting Euler–Lagrange equations are then solved to obtain the equations of motion. The model is validated using experimental data from a virtual reality crossing simulation with human participants. We thus conclude that the least action principle provides a useful tool in the study of interceptive walking.

scholarly journals Galaxy Rotation Curves in Covariant Hořava-Lifshitz Gravity

Galaxies ◽  
2013 ◽  
Vol 2 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Jean Alexandre ◽  
Martyna Kostacinska
Keyword(s):  
Rotation Curves ◽  
Galaxy Rotation Curves
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