scholarly journals Snyder-like modified gravity in Newton's spacetime

2018 ◽  
Vol 27 (07) ◽  
pp. 1850070
Author(s):  
Carlos Leiva
Keyword(s):  
Modified Gravity ◽  
Kepler Problem ◽  
Dynamic Equations ◽  
Integrals Of Motion ◽  
Curved Spacetime ◽  
Length Dependence ◽  
Fundamental Length ◽  
Deformed Algebra ◽  
Torsion Free

This work is focused on searching a geodesic interpretation of the dynamics of a particle under the effects of a Snyder-like deformation in the background of the Kepler problem. In order to accomplish that task, a Newtonian spacetime is used. Newtonian spacetime is not a metric manifold, but allows to introduce a torsion-free connection in order to interpret the dynamic equations of the deformed Kepler problem as geodesics in a curved spacetime. These geodesics and the curvature terms of the Riemann and Ricci tensors show a mass and a fundamental length dependence as expected, but are velocity-independent that is a feature present in other classical approaches to the problem. In this sense, the effect of introducing a deformed algebra is examined and the corresponding curvature terms calculated, as well as the modifications of the integrals of motion.

scholarly journals MICZ-Kepler systems in noncommutative space and duality of force laws

2014 ◽  
Vol 29 (32) ◽  
pp. 1450187 ◽  
Author(s):  
Partha Guha ◽  
E. Harikumar ◽  
N. S. Zuhair
Keyword(s):  
Deformation Parameter ◽  
Kepler Problem ◽  
Space Time ◽  
Integrable Models ◽  
Noncommutative Space ◽  
Two Dimensional ◽  
Integrals Of Motion ◽  
Sundman Transformation ◽  
Two Systems ◽  
Commutative Space

In this paper, we analyze the modification of integrable models in the κ-deformed space–time. We show that two-dimensional isotropic oscillator problem, Kepler problem and MICZ-Kepler problem in κ-deformed space–time admit integrals of motion as in the commutative space. We also show that the duality equivalence between κ-deformed Kepler problem and κ-deformed two-dimensional isotropic oscillator explicitly, by deriving Bohlin–Sundman transformation which maps these two systems. These results are valid to all orders in the deformation parameter.

Jordan k-Homomorphisms onto Completely Prime ΓN Rings

1970 ◽  
Vol 30 ◽  
pp. 32-40
Author(s):  
Sujoy Charaborty ◽  
Akhil Chandra Paul
Keyword(s):  
Torsion Free

By introducing the notions of k-homomorphism, anti-k-homomorphism and Jordan khomomorphism of Nobusawa Γ -rings, we establish some significant results related to these concepts. If M1 is a Nobusawa Γ1 -ring and M2 is a 2-torsion free completely prime Nobusawa Γ2 -ring, then we prove that every Jordan k-homomorphism θ of M1 onto M2 such that k(Γ1 ) = Γ2 is either a k-homomorphism or an anti-k-homomorphism. GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 30 (2010) 32-40 DOI: http://dx.doi.org/10.3329/ganit.v30i0.8500  

Recognition of Neurons Impulses with the Use of Nonlinear Dynamic Equations

2001 ◽  
Vol 33 (5-8) ◽  
pp. 10
Author(s):  
Tatyana I. Aksenova ◽  
Igor V. Tetko ◽  
Olga K. Chibirova ◽  
Alexandro Villa
Keyword(s):  
Nonlinear Dynamic ◽  
Dynamic Equations ◽  
Nonlinear Dynamic Equations

GRAVITY CAN BE OBSERVED IN THE ABSENCE OF CURVED SPACETIME, THUS CURVED SPACETIME IS NOT RESPONCIBLE FOR GRAVITY

2015 ◽  
Vol 8 (1) ◽  
pp. 1976-1981
Author(s):  
Casey McMahon
Keyword(s):  
General Relativity ◽  
Special Relativity ◽  
Relative Position ◽  
Gravitational Force ◽  
Curved Spacetime ◽  
Relative Time ◽  
Curved Space ◽  
Spacetime Curvature ◽  
Equivalence Model ◽  
The Universe

The principle postulate of general relativity appears to be that curved space or curved spacetime is gravitational, in that mass curves the spacetime around it, and that this curved spacetime acts on mass in a manner we call gravity. Here, I use the theory of special relativity to show that curved spacetime can be non-gravitational, by showing that curve-linear space or curved spacetime can be observed without exerting a gravitational force on mass to induce motion- as well as showing gravity can be observed without spacetime curvature. This is done using the principles of special relativity in accordance with Einstein to satisfy the reader, using a gravitational equivalence model. Curved spacetime may appear to affect the apparent relative position and dimensions of a mass, as well as the relative time experienced by a mass, but it does not exert gravitational force (gravity) on mass. Thus, this paper explains why there appears to be more gravity in the universe than mass to account for it, because gravity is not the resultant of the curvature of spacetime on mass, thus the “dark matter” and “dark energy” we are looking for to explain this excess gravity doesn’t exist.

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