Related papers: Possible potentials responsible for stable circula…
Relativistic tidal equations are formulated with respect to the rest frame of a central gravitational source and their solutions are studied. The existence of certain relativistic critical tidal currents are thereby elucidated.…
The potential concept that is successful in classical electrodynamics should also be applicable to the nonlinear electromagnetic forces acting on matter. The obvious method of determining these potentials should be provided by Helmholtz's…
As gravity is a long-range force, it is {\it a priori} conceivable that the Universe's global matter distribution select a preferred rest frame for local gravitational physics. At the post-Newtonian approximation, the phenomenology of…
The methods of conformal field theory are used to obtain the series of exact solutions of the fundamental equations of the theory of turbulence. The basic conjecture, proved to be self-consistent ,is the conformal invariance of the inertial…
We consider the spatial central force problem with a real analytic potential. We prove that for all analytic potentials, but the Keplerian and the Harmonic ones, the Hamiltonian fulfills a nondegeneracy property needed for the applicability…
Recently Mansuripur has called into question the validity of the Lorentz force in connection with relativistic electromagnetic theory. Here we present some very simple point-charge systems treated through order v^{2}/c^{2} in order to…
I find conditions under which the "Weak Energy Principle" of Katz, Inagaki and Yahalom (1993) gives necessary and sufficient conditions. My conclusion is that, necessary and sufficient conditions of stability are obtained when we have only…
In this work we show that a relativistic spinning particle can be described at the classical and the quantum level as being composed of two physical constituents which are entangled and separated by a fixed distance. This bilocal model for…
The stability properties of relativistic stars against gravitational collapse to black hole is a classical problem in general relativity. A sufficient criterion for secular instability was established by Friedman, Ipser and Sorkin (1988),…
Euler's three-body problem is the problem of solving for the motion of a particle moving in a Newtonian potential generated by two point sources fixed in space. This system is integrable in the Liouville sense. We consider the Euler problem…
We investigate the motion in space of an infinitesimal particle in the gravitational field generated by three primary bodies positioned at the vertices of a fixed equilateral triangle. We assume that the distances between the primaries are…
This article reports on emergence of structures in a class of alternative theories of gravity. These theories do not have any horizon, flatness, initial cosmological singularity and (possibly) quantization problems. The model is…
We study the stability of static, spherically symmetric solutions of Rastall's theory in the presence of a scalar field with respect to spherically symmetric perturbations. It is shown that the stability analysis is inconsistent in the…
This first of two papers is a speculation on the nature of Mach's Principle, derived from the formulation of two questions: (A) Can a globally inertial space and time be associated with a non-trivial global matter distribution? (B) If so,…
We establish the existence of non-constant periodic solutions to the Lorentz force equation, where no scalar potential is needed to induce the electromagnetic field. Our results extend to cases where a possibly singular scalar potential is…
The logarithm function is the gravitational potential in $\mathbb{R}^2$. We prove that the logarithm central force problem is block regularizable, that is, the (incomplete) flow may be continuously extended over the singularity at the…
Spacetime and internal symmetries can be used to severely restrict the form of the equations for the fundamental laws of physics. The success of this approach in the context of general relativity and particle physics motivates the…
Given some assumptions it is possible to derive the most general post-general relativistic theory of gravity for the distant field of a point mass. The force law derived from this theory contains a Rindler term in addition to well-known…
We consider a class of attractive-repulsive energies, given by the sum of two nonlocal interactions with power-law kernels, defined over sets with fixed measure. It has recently been proved by R. Frank and E. Lieb that the ball is the…
The relativistic two-body potentials of constraint theory for systems composed of two spin-0 or two spin-1/2 particles are calculated, in perturbation theory, by means of the Lippmann-Schwinger type equation that relates them to the…