Related papers: A Mond Programme from Einstein Hilbert Action
The covariant canonical transformation theory applied to the relativistic Hamiltonian theory of classical matter fields in dynamical space-time yields a novel (first order) gauge field theory of gravitation. The emerging field equations…
The starting point of this work is the original Einstein action, sometimes called the Gamma squared action. Continuing from our previous results, we study various modified theories of gravity following the Palatini approach. The metric and…
The Hamiltonian for physical systems and dynamic geometry generates the evolution of a spatial region along a vector field. It includes a boundary term which not only determines the value of the Hamiltonian, but also, via the boundary term…
We consider a simplified model of quantum gravity using a mini-superspace description of an isotropic and homogeneous universe with dust. We derive the corresponding Friedmann equations for the scale factor, which now contain a dependence…
Modified Newtonian dynamics (MOND) and similar proposals can (at least partially) explain the excess rotation of galaxies or the equivalent mass-discrepancy acceleration, without (or by reducing) the requirement of dark matter halos. This…
We investigate particle laws of motion derived from nonstandard kinetic actions of a special form. We are guided by a phenomenological scheme--the modified dynamics (MOND)--that imputes the mass discrepancy observed in galactic systems to a…
General Relativity is able to describe the dynamics of galaxies and larger cosmic structures only if most of the matter in the Universe is dark, namely it does not emit any electromagnetic radiation. Intriguingly, on the scale of galaxies,…
The Weiss variational principle in mechanics and classical field theory is a variational principle which allows displacements of the boundary. We review the Weiss variation in mechanics and classical field theory, and present a novel…
The main goal of this paper is to get in a straightforward form the field equations in metric f(R) gravity, using elementary variational principles and adding a boundary term in the action, instead of the usual treatment in an equivalent…
We address the question of ambiguity in defining a Hamiltonian for a scalar field. We point out that the Hamiltonian for a real Klein-Gordon scalar field must be consistent with the energy density obtained from the Schrodinger equation in…
The usual derivation of Einstein's field equations from the Einstein--Hilbert action is performed by silently assuming the metric tensor's symmetric character. If this symmetry is not assumed, the result is a new theory, such as Einstein's…
We looked at the orbital motions of test particles according to the External Field Effect (EFE) predicted by the MOdified Newtonian Dynamics (MOND) in the Oort cloud which falls in the deep MONDian regime (r\approx 50-150 kAU). Concerning…
We provide a new extension of general relativity (GR) which has the remarkable property of being more constrained than GR plus a cosmological constant, having one less free parameter. This is implemented by allowing the cosmological…
The expressions of momentum and energy of a particle in special relativity are often derived in a quite unconvincing manner in elementary text, by resorting either to electrodynamic or quantum considerations, or via the introduction of the…
Einstein-Hilbert action and its natural generalizations to higher dimensions (like the Lanczos-Lovelock action) have certain peculiar features. All of them can be separated into a bulk and a surface term, with a specific ("holographic")…
Cosmic acceleration can be achieved not only with a sufficiently flat scalar field potential but through kinetic terms coupled to gravity. These derivative couplings impose a shift symmetry on the scalar field, aiding naturalness. We write…
MOND dynamics consists of a modification of the acceleration with respect to the one provided by Newtonian mechanics. In this paper we investigate whether it can be derived from a velocity-dependent deformation of the coordinates of the…
We construct the covariant nonlocal action for recently suggested long-distance modifications of gravity theory motivated by the cosmological constant and cosmological acceleration problems. This construction is based on the special…
Universe evolution, as described by Friedmann's equations, is determined by source terms fixed by the choice of pressure $\times$ energy-density equations of state $p(\rho)$. The usual approach in Cosmology considers equations of state…
According to the formal holographic principle, a modification to the assumption of holographic principle in Verlinder's investigation of entropy force is obtained. A more precise relation between entropy and area in the holographic system…