Related papers: Energy for N-Body Motion in Two Dimensional Gravit…
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…
In this paper, we introduce a deterministic approach of quantum mechanics for particles with spin 1 2 moving in one dimension. We present a Lagrangian of a spinning particle ($s ={1 \over 2} $), and deduce the expression of the conjugate…
We consider a gravitational model in which matter is non-minimally coupled to geometry, with the effective Lagrangian of the gravitational field being given by an arbitrary function of the Ricci scalar, the trace of the matter…
Like the Lovelock Lagrangian which is a specific homogeneous polynomial in Riemann curvature, for an alternative derivation of the gravitational equation of motion, it is possible to define a specific homogeneous polynomial analogue of the…
An extension to the Einstein-Cartan (EC) action is discussed in terms of cosmological solutions. The torsion incorporated in the EC Lagrangian is assumed to be totally anti-symmetric, represented by a time-like axial vector $S^\mu$. The…
We establish a general relation between the canonical energy-momentum tensor of Lagrangian dynamics and the tensor that acts as the source of the gravitational field in Einstein's equations, and we show that there is a discrepancy between…
It is shown that the reduced particle dynamics of 2+1 dimensional gravity in the maximally slicing gauge has hamiltonian form. This is proved directly for the two body problem and for the three body problem by using the Garnier equations…
Any connection between dark matter and extra dimensions can be cognizably evinced from the associated effective energy-momentum tensor. In order to investigate and test such relationship, a higher dimensional spacetime endowed with a…
We present a framework for discussing the cosmology of dark energy and dark matter based on two scalar degrees of freedom. An effective field theory of cosmological perturbations is employed. A unitary gauge choice renders the dark energy…
In the present work, torsion energy is defined. Its law of conservation is given. It is shown that this type of energy gives rise to a repulsive force which can be used to interpret supernovae type Ia observations, and consequently the…
This paper elaborates the problem of energy-momentum in the framework of teleparallel equivalent of General Relativity. For this purpose, we consider energy-momentum prescription derived from the integral form of the constraint equations…
The Lagrangian, the Hamiltonian and the constant of motion of the gravitational attraction of two bodies when one of them has variable mass is considered. The relative and center of mass coordinates are not separated, and choosing the…
We demonstrate that there does exist an equilibrium description of thermodynamics on the apparent horizon in the expanding cosmological background for a wide class of modified gravity theories with the Lagrangian density $f(R, \phi, X)$,…
In the relativistic uniform model for continuous medium the integral theorem of generalized virial is derived, in which generalized momenta are used as particles momenta. This allows us to find exact formulas for the radial component of the…
New, gauge-independent, second-order Lagrangian for the motion of classical, charged test particles is used to derive the corresponding Hamiltonian formulation. For this purpose a Hamiltonian description of the theories derived from the…
There are well-known problems associated with the idea of (local) gravitational energy in general relativity. We offer a new perspective on those problems by comparison with Newtonian gravitation, and particularly geometrized Newtonian…
In a foregoing paper, gravity has been interpreted as the pressure force exerted on matter at the scale of elementary particles by a perfect fluid. Under the condition that Newtonian gravity must be recovered in the incompressible case, a…
We generalise a recent derivation of the relativistic expressions for momentum and kinetic energy from the one-dimensional to the three-dimensional case.
We study two-bodies gravitational problem where the mass of one of the bodies varies and suffers a damping-antidamping effect due to star wind during its motion. A constant of motion, a Lagrangian and a Hamiltonian are given for the radial…
With the post-Newtonian approxination, the energy of Schwarzschild spacetime in the Weinberg prescription is obtained. The energy for the first post-Newtonian approximation $E^{(1)} = m$ gives the Newtonian treatment of Schwarzschild…