Related papers: Conformally Flat Metric, Position-Dependent Mass a…
We analyze the dynamical equations obeyed by a classical system with position-dependent mass. It is shown that there is a non-conservative force quadratic in the velocity associated to the variable mass. We construct the Lagrangian and the…
Models of relativistic particle with Lagrangian ${\cal L}(k_1)$, depending on the curvature of the worldline $k_1$, are considered. By making use of the Frenet basis, the equations of motion are reformulated in terms of the principal…
We consider f(R,T) modified theory of gravity, in which the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar and the trace of the energy-momentum tensor of the matter, in order to investigate the dark-matter…
A geometric theory for spacetimes whose world lines associated with physical particles have an upper bound for the proper acceleration is developed. After some fundamental remarks on the requirements that the classical dynamics for point…
A Lagrangian formalism is used to study the motion of a spinning massive particle in Friedmann--Robertson--Walker and G\"odel spacetimes, as well as in a general Schwarzschild-like spacetime and in static spherically symmetric conformally…
In particle physics, most of the classical models consider that the centre of mass and centre of charge of an elementary particle, are the same point. This presumes some particular relationship between the charge and mass distribution, a…
Newton second law of dynamics is a law of motion but also a useful definition of force (F=MA) or inertial mass (M=F/A), assuming a definition of acceleration and parallelism of force and acceleration. In the special theory of relativity,…
In relativistic mechanics the energy-momentum of a free point mass moving without acceleration forms a four-vector. Einstein's celebrated energy-mass relation E=mc^2 is commonly derived from that fact. By contrast, in Newtonian mechanics…
The non-gauge vector field with as simple as possible Lagrangian (\ref{Lagrangian}) turned out an adequate tool for macroscopic description of the main properties of dark matter. The dependence of the velocity of a star on the radius of the…
We propose a gravitational theory in which the effective Lagrangian of the gravitational field is given by an arbitrary function of the Ricci scalar, the trace of the matter energy-momentum tensor, and the contraction of the Ricci tensor…
The problem of point particle in the 1/r gravitational field was studied in SR-based Mechanics. Equations of motion under assumption of field dependent proper mass were obtained in the relativistic Lagrangean framework. The dependence of…
We generalize previous work by considering a novel gravitational model with an action given by an arbitrary function of the Ricci scalar, the matter Lagrangian density, a scalar field and a kinetic term constructed from the gradients of the…
The equations of motion for a Lagrangian ${\cal L}(k_1)$, depending on the curvature $k_1$ of the particle worldline, embedded in a space--time of constant curvature, are considered and reformulated in terms of the principal curvatures. It…
A novel theory of $F(R)$ gravity with the Lagrangian density ${\cal L}=[R-(b/\beta)\arctan\left(\beta R\right)]/(2\kappa^2)$ is analyzed. Constant curvature solutions of the model are found, and the potential of the scalar field and the…
For a one-dimensional conservative systems with position depending mass, one deduces consistently a constant of motion, a Lagrangian, and a Hamiltonian for the non relativistic case. With these functions, one shows the trajectories on the…
The Lagrangian density of standard relativistic mean-field (RMF) models with density-dependent meson-nucleon coupling vertices is modified by introducing couplings of the meson fields to derivative nucleon densities. As a consequence, the…
The determination of the velocities, accelerations and the gravitational field intensity at a given location in a galaxy could potentially be achieved in an unexpected manner with the environment of the observer, for instance, the local…
We consider a class of modified gravity models where the terms added to the standard Einstein-Hilbert Lagrangian are just a function of the metric only. For linearized perturbations around an isotropic space-time, this class of models is…
We investigate the possibility to construct a generalization of the Standard Model, which we call the Maximal Mass Model because it contains a limiting mass $M$ for its fundamental constituents. The parameter $M$ is considered as a new…
We consider the growth rate of matter perturbations in the Einstein dark energy theory. The theory consists of the Einstien-Hilbert Lagrangian plus the trace of the energy momentum tensor, coupled non-minimally to a dynamical vector field.…