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We set up a model of an electric charge where the noninvertible metric phase of first order gravity supercedes the point charge singularity in a curved spacetime. A topological interpretation of the electric charge is provided in terms of…
The vacuum polarization energy is the leading quantum correction to the classical energy of a soliton. We study this energy for two-component solitons in one space dimension as a function of the soliton's topological charge. We find that…
Exact wave functions are is derived from an azimuthally periodic a self-consistent quantum Hamiltonian in 2+1 dimensions using both the Klein-Gordon and the Schroedinger equations. It isWe shown that, curiously, for both relativistic and…
In presence of magnetic fields, the orbits of charged particles can be displaced from the equatorial plane. We study circular orbits of electrically charged massive objects around a magnetic black hole in the probe approximation. We show…
The exact Li$\acute{e}$nard-Wiechert solutions for the point charge in arbitrary motion are shown to be null fields everywhere. These are used as a basis to introduce extended electromagnetic field equations that have null field solutions…
Closed-Form Kepler solutions in projective coordinates are used to define a corresponding set of eight orbit elements and obtain their governing equations for arbitrarily-perturbed two-body dynamics. The elements and their dynamics are…
A new class of solutions which yields an $(n+1)$-dimensional spacetime with a longitudinal nonlinear magnetic field is introduced. These spacetimes have no curvature singularity and no horizon, and the magnetic field is non singular in the…
The energy of extended classical objects, such as vortices, depends on their shape. In particular, we show that the curvature energy of a kink in two spatial dimensions, as a prototype of extended classical solutions, is always negative. We…
The quantum properties of localized finite energy solutions to classical Euler-Lagrange equations are investigated using the method of collective coordinates. The perturbation theory in terms of inverse powers of the coupling constant $g$…
The Bertrand's theorem is extended, i.e. closed orbits still may exist for other central potentials than the power law Coulomb potential and isotropic harmonic oscillator. It is shown that for the combined potential $V(r)=W(r)+b/r^2$…
This paper explores the problem of analytically approximating the orbital state for a subset of orbits in a rotating potential with oblateness and ellipticity perturbations. This is done by isolating approximate differential equations for…
We solve the stationary Schr\"odinger equation for a particle confined to a 3D spherical wedge -- the region $\{(r,\theta,\phi): 0 \leq r \leq R,\, 0 \leq \theta \leq \pi,\, 0 \leq \phi \leq \Phi\}$ with Dirichlet BCs on all surfaces. This…
In the present work, we study the classical behavior of an electric dipole in presence of an external uniform magnetic field. We derive equations and constants of motion from the Lagrangian formulation. We obtain an infinitely periodic…
We study the regularity properties of the solutions to the nonlinear equation with fractional diffusion $$ \partial_tu+(-\Delta)^{\sigma/2}\varphi(u)=0, $$ posed for $x\in \mathbb{R}^N$, $t>0$, with $0<\sigma<2$, $N\ge1$. If the…
A particle of mass $\mu$ moves on a circular orbit of a nonrotating black hole of mass $M$. Under the restrictions $\mu/M \ll 1$ and $v \ll 1$, where $v$ is the orbital velocity, we consider the gravitational waves emitted by such a binary…
A new approach to approximate the kinetic-energy-functional dependent component ($v_t[\rho_A,\rho_B](\vec{r})$) of the effective potential in one-electron equations for orbitals embedded in a frozen density environment (Eqs. 20-21 in…
It is known that for some time periodic potentials $q(t, x) \geq 0$ having compact support with respect to $x$ some solutions of the Cauchy problem for the wave equation $\partial_t^2 u - \Delta_x u + q(t,x)u = 0$ have exponentially…
We present a new approach to the problem of binary black holes in the pre-coalescence stage, i.e. when the notion of orbit has still some meaning. Contrary to previous numerical treatments which are based on the initial value formulation of…
We first obtain the electric and magnetic fields corresponding to a `spin'-orbit classical interaction of a r^2 potential. Assuming that Maxwell equations hold for these fields, we infer the conditions on the `spin' vector forbidding…
The formalism of classical particle dynamics is reinvestigated according to the basic requirement of causal consistency, and a new equation of particle dynamics, which is more general and more in line with classical mechanics experiments…