Related papers: Does Newtonian dynamics need Euclidean space?
We analyse the non-linear gravitational dynamics of a pressure-less fluid in the Newtonian limit of General Relativity in both the Eulerian and Lagrangian pictures. Starting from the Newtonian metric in the Poisson gauge, we transform to…
In the standard approach to studying cosmological structure formation, the overall expansion of the Universe is assumed to be homogeneous, with the gravitational effect of inhomogeneities encoded entirely in a Newtonian potential. A topic…
In the context of modified Newtonian dynamics, the fundamental plane, as the observational signature of the Newtonian virial theorem, is defined by high surface brightness objects that deviate from being purely isothermal: the line-of-sight…
In a recent paper by Ambr\'osio et al. [arXiv:2405.14799], it was shown that the gravitational force law of the Modified Newtonian Dynamics (MOND) phenomenology can be derived within the framework of entropic gravity and the holographic…
It seems likely that the generalized Einstein equations are not complete and only partly account for the effect on the Universe dynamics of that part of the energy of the space environment the change of which is purely geometric. There are…
We extend the thermodynamic derivation of gravity in the Jacobson framework by generalizing the Clausius relation through a nontrivial entropy functional. We show that entropy deformations appear as modifications of the effective…
The $n$ integrals in involution for the motion on the $n$-dimensional ellipsoid under the influence of a harmonic force are explicitly found. The classical separation of variables is given by the inverse momentum map. In the quantum case…
In most text books of mechanics, Newton's laws or Hamilton's equations of motion are first written down and then solved based on initial conditions to determine the constants of the motions and to describe the trajectories of the particles.…
An earlier paper [1] presented a gravity theory based on the optics of de Broglie waves rather than curved space-time. While the universe's geometry is flat, it agrees with the standard tests of general relativity. A second paper [2] showed…
We illustrate why a space-time structure as in General Relativity is not in contradiction with a dynamical origin of gravity from a scalar field. Further, we argue that the recently discovered gap-less mode of the singlet Higgs field…
It is widely accepted that the notion of an inertial frame is central to Newtonian mechanics and that the correct space-time structure underlying $\text{Newton's}$ methods in $\textit{Principia}$ is neo-Newtonian or Galilean space-time. I…
We are studying the dynamics of a one-dimensional field in a non-commutative Euclidean space. The non-commutative space we consider is the one that emerges in the context of three dimensional Euclidean quantum gravity: it is a deformation…
A correspondence between the Equivalence principle and the homogeneity of the universe is discussed. In Newtonian gravity, translation of co-moving coordinates in a uniformly expanding universe defines an accelerated frame. A consistency…
The Newton equation describing the particle motion in constant external field force on canonical, Lie-algebraic and quadratic space-time is investigated. We show that for canonical deformation of space-time the dynamical effects are absent,…
An elementary derivation of the Newton "inverse square law" from the three Kepler laws is proposed. Our proof, thought essentially for first-year undergraduates, basically rests on Euclidean geometry. It could then be offered even to…
An alternative derivation of generalized gravitational entropy associated to co-dimension 2 'entangling' hypersurfaces is given. The approach is similar to the Jacobson-Myers 'Hamiltonian' method and it does not require computations on…
Based on the Generalized Principle of Inertia, which states that: \emph{An inanimate object moves freely, that is, with zero acceleration, in its own spacetime, whose geometry is determined by all of the forces affecting it,} we geometrize…
In this work we derive general quantum phenomenological equations of gravitational dynamics and analyse its features. The derivation uses the formalism developed in thermodynamics of spacetime and introduces low energy quantum gravity…
Within the context of Newton's theory of gravitation, restricted to point-like test particles and central bodies, stable circular orbits in ordinary space are related to stable circular paths on a massless, unmovable, undeformable…
The growing availability of increasingly accurate data on transiting exoplanets suggests the possibility of using these systems as possible testbeds for modified models of gravity. In particular, we suggest that the post-Keplerian (pK)…