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We present exact analytical solutions of the Dirac equation in $(1+1)$-dimensions for the generalized Kratzer potential by taking the pseudoscalar interaction term as an attractive Coulomb potential. We study the problem for a particular…
There are constructed exact solutions of the quantum-mechanical Dirac equation for a spin S=1/2 particle in Riemannian space of constant negative curvature, hyperbolic Lobachevsky space, in presence of an external magnetic field, analogue…
In this paper we consider the central force problem in the special theory of relativity. We derive the special relativistic version of the Binet equation describing the orbit of a body. Then, the motion of a planet in a solar-like system…
The electromagnetic self-force of a point charge moving arbitrarily on a rectilinear trajectory is calculated by averaging its retarded electric self-field over a sphere of infinitesimal radius centered on the charge's present position. The…
Electrodynamics for self-interacting scalar fields in spatially flat Friedmann-Robertson-Walker space-times is studied. The corresponding one-loop field equation for the expectation value of the complex scalar field in the conformal vacuum…
The complex method to obtain 2-dimensional Born-Infeld electrostatic solutions is presented in a renewed form. The solutions are generated by a holomorphic seed that makes contact with the Coulombian complex potential. The procedure is…
Introducing a radially dependent magnetic field into Newton's off-center circular orbits potential so as to preserve the $E=0$ dynamical symmetry leads to a unique choice of field that can be identified as the inclusion of a magnetic…
A spherically symmetric charged ideal fluid solution of Einstein field equation is given in the presence of the cosmological constant and two well known example of this type of solution is presented. If the matter is confined in a region,…
Motivated by a recent analysis which presents explicitly the general solution, we consider the eigenvalue problem of the spinless Salpeter equation with a ("hard-core amended") Coulomb potential in one dimension. We prove the existence of a…
During the past century, there has been considerable discussion and analysis of the motion of a point charge, taking into account "self-force" effects due to the particle's own electromagnetic field. We analyze the issue of "particle…
We compute the self-force acting on an electric charge at rest in Schwarzschild-de Sitter spacetimes, allowing the cosmological constant to be either positive or negative. In the case of a positive cosmological constant, we show that the…
The region very close to an electron ($r << r_0 = e^2/mc^2 \approx 2.8\times 10^{-13}$ cm) is, according to quantum electrodynamics, a seething maelstrom of virtual electron-positron pairs flashing in and out of existence. To take account…
We present a study of planar physical solutions to the Lorentz-Dirac equation in a constant electromagnetic field. In this case, we reduced the Lorentz-Dirac equation to the one second order differential equation. We obtained the…
We study spherically symmetric static empty space solutions in $R+\varepsilon/R$ model of $f(R)$ gravity. We show that the Schwarzschild metric is an exact solution of the resulted field equations and consequently there are general…
We study the dynamics near the central singularity in spherically symmetric collapse of a massless scalar field toward Schwarzschild black hole formation. The equations of motion take different simplified forms in the early and late stages…
We present an interaction modeling for the relativistic spin-0 charged particles moving in a uniform magnetic field. In the absence of an improved perturbative way, we solve directly Kummer's differential equation including principal…
We consider the problem of a rotating charged spherical shell of radius a carrying an axially symmetric distribution of charge. We give the interior and exterior solutions to this problem for arbitrary zonal dependence of the surface charge…
The usual equation for both motions of a single planet around the sun and electrons in the deterministic Rutherford-Bohr atomic model is conservative with a singular potential at the origin. When a dissipation is added, new phenomena…
We report on a remarkable class of exact solutions to force-free electrodynamics that has four-current along the light cones of an arbitrary timelike worldline in flat spacetime. No symmetry is assumed, and the solutions are given in terms…
We study a special case at which the analytical solution of the Lippmann-Schwinger integral equation for the partial wave two-body Coulomb transition matrix for likely charged particles at negative energy is possible. With the use of the…