Related papers: Newton's superb theorem: An elementary geometric p…
We discuss theories with inverse powers of the Ricci scalar. We find the exact metric produced by point masses in these theories, and show that the gravitational force between static objects is consistent with experiments.
Newton's second law has limited scope of application when transient phenomena are present. We consider a modification of Newton's second law in order to take into account a sudden change (surge) of angular momentum or linear momentum. We…
Physicists believe, with some justification, that there should be a correspondence between familiar properties of Newtonian gravity and properties of solutions of the Einstein equations. The Positive Mass Theorem (PMT), first proved over…
We describe a geometric and symmetry-based formulation of the equivalence principle in non-relativistic physics. It applies both on the classical and quantum levels and states that the Newtonian potential can be eliminated in favor of a…
Application of Newton's ideas from "Principia" gives many new results in mechanics. Here we explore the question ``What form of extra force will maintain the magnitude of a vector constant of the motion while changing its direction?''
Kepler's laws of planetary motion are acknowledged as highly significant to the construction of universal gravitation. The present study demonstrates different ways to derive the law of equal areas for the Earth by general geometrical and…
Classical Newtonian gravitational theory does not satisfy the causality principle because it is based on instantaneous action-at-a-distance. A causal version of Newtonian theory for a large rotating sphere is derived herein by…
This work shows that, Newton's Proposition 1 in the {\it Principia}, is an {\it exact} graphical representation of a canonical transformation, a first-order symplectic integrator generated at a finite time-step by the Hamiltonian. A…
A scalar theory of gravitation with a preferred reference frame (PRF) is considered, that accounts for special relativity and reduces to it if the gravitational field cancels. The gravitating system consists of a finite number of…
The nonsymmetric gravitational theory predicts an acceleration law that modifies the Newtonian law of attraction between particles. For weak fields a fit to the flat rotation curves of galaxies is obtained in terms of the mass…
A n-time generalization of Newton's law (of universal gravitation) formula in N =n + d + 1-dimensional space-time is conjectured. This formula implies a relation for effective N-dimensional gravitational constant G_{eff} = G cos^2 \theta,…
Understanding the deflection of light by a massive deflector, as well as the associated gravitational lens phenomena, require the use of the theory of General Relativity. I consider here a classical approach, based on Newton's equation of…
Conformal geometry is considered within a general relativistic framework. An invariant distant for proper time is defined and a parallel displacement is applied in the distorted space-time, modifying Einstein's equation appropriately. A…
A surprising, gravity related Verlinde-conjecture, that generated immense interest, asserts that gravity is an emergent entropic force. We provided a classical proof of the assertion in [doi.org/j.physa.2018.03.019]. Here, we classically…
Corrections to Newton's inverse law have been so far considered, but not clear in warped higher dimensional worlds, because of complexity of the Einstein equation. Here we give a model of a warped 6D world with an extra 2D sphere. We take a…
In the standard model the mass of elementary particles is considered as a dynamical property emerging from their interaction with the Higgs field. We show that this assumption implies peculiar deviations from the law of universal…
We consider the Newtonian limit of modified theories of gravity that include inverse powers of the curvature in the action in order to explain the cosmic acceleration. It has been shown that the simplest models of this kind are in conflict…
In this work we show that corrections to the Newton's second law appears if we assume that the phase space has a symplectic structure consistent with the rules of commutation of noncommutative quantum mechanis. In the central field case we…
Guided by the Einstein equivalence principle that identifies the phenomenon of gravitation as a manifestation of the dynamics of spacetime in contrast to a localizable force, we review and explore its consequences on formulating a theory of…
This paper has been withdrawn by the author after further work showed the proposed theoretical approach cannot fit planetary perihelion precession data. As presented, the theory doesn't fit gravitational light deflection by the sun either,…