Related papers: Note on "Electromagnetism and Gravitation"
When a set of particles are moving in a potential field, two aspects are concerned: 1) the relative motion of particle in spatial domain; 2) the particle velocity variations in time domain. The difficulty on treating the systems is…
We give a systematic method for discretizing Hamiltonian partial differential equations (PDEs) with constant symplectic structure, while preserving their energy exactly. The same method, applied to PDEs with constant dissipative structure,…
Dissipative Lagrangians and Hamiltonians having Coulomb, viscous and quadratic damping,together with gravitational and elastic terms are presented for a formalism that preserves the Hamiltonian as a constant of the motion. Their derivations…
The paper studies the validity of Maxwell equation in the case for coexistence of electromagnetic field and gravitational field. With the algebra of quaternions, the Newton's law of gravitation is the same as that in classical theory of…
Gyrokinetic field theory is addressed in the context of a general Hamiltonian. The background magnetic geometry is static and axisymmetric, and all dependence of the Lagrangian upon dynamical variables is in the Hamiltonian or in free field…
Part A of this article is devoted to the general investigation of the gravitational-wave emission by post-Newtonian sources. We show how the radiation field far from the source, as well as its near-zone inner gravitational field, can (in…
Most classical mechanical systems are based on dynamical variables whose values are real numbers. Energy conservation is then guaranteed if the dynamical equations are phrased in terms of a Hamiltonian function, which then leads to…
We obtain a generally covariant conservation law of energy-momentum for gravitational anyons by the general displacement transform. The energy-momentum currents have also superpotentials and are therefore identically conserved. It is shown…
We propose a gravitational energy-momentum tensor of the general relativity obtained using Noethers theorem. It transforms as a tensor under general coordinate transformations. One of the two indices of the gravitational energy-momentum…
The individuation of point-events and the Hamiltonian way of distinguishing gravitational from inertial effects in general relativity are discussed.
Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. In an accompanying paper I, we analyzed this theory and summarized it in nine…
We study a noncommutative deformation of general relativity where the gravitational field is described by a matrix-valued symmetric two-tensor field. The equations of motion are derived in the framework of this new theory by varying a…
Gravity, and the puzzle regarding its energy, can be understood from a gauge theory perspective. Gravity, i.e., dynamical spacetime geometry, can be considered as a local gauge theory of the symmetry group of Minkowski spacetime: the…
We develop a general stability theory for equilibrium points of Poisson dynamical systems and relative equilibria of Hamiltonian systems with symmetries, including several generalisations of the Energy-Casimir and Energy-Momentum methods.…
Integrating equations of particle-number and energy-momentum conservation and Maxwell field equations, we study the oscillation and drift of electron and positron pairs coherently with fields after these pairs are produced in external…
We give sufficient conditions for the rigid body in the presence of an axisymmetric force field and a gyroscopic torque to admit a Hamilton-Poisson formulation. Even if by adding a gyroscopic torque we initially lose one of the conserved…
We present a continuity equation for the gravitational energy-momentum, which is obtained in the framework of the teleparallel equivalent of general relativity. From this equation it follows a general definition for the gravitational…
The gravitational energy shift for photons is extended to all mass-equivalent energies $E = mc^2$, obeying the quantum condition $E = h\nu$.On an example of a relativistic binary system, it was shown that the gravitational energy shift…
Using the Einstein gravitation theory we show how to obtain the basic equations which predict the gravitational waves. This paper was written to graduate and post-graduate students of Physics. We deduce the equations didactically following…
Basic principles of the Hamilton approach developed for the metric General Relativity (Einstein`s GR) are discussed. In particular, we derive the Hamiltonian of the metric GR in the explicit form. This Hamiltonian is a quadratic function of…