Related papers: Weighted energy problem on the unit sphere
Charged axially symmetric solution of the coupled gravitational and electromagnetic fields in the tetrad theory of gravitation is derived. The metric associated with this solution is an axially symmetric metric which is characterized by…
We consider the total energy decay together with L^2-bound of the solution itself of the Cauchy problem for wave equations with a localized damping and a short-range potential. We treat it in the one dimensional Euclidean space R. We adopt…
The Schr\"odinger equation for a charged particle in the field of a nonrelativistic electric quadrupole in two dimensions is known to be separable in spherical coordinates. We investigate the occurrence of bound states of negative energy…
A novel energy minimization formulation of electrostatics that allows computation of the electrostatic energy and forces to any desired accuracy in a system with arbitrary dielectric properties is presented. An integral equation for the…
By using the generalized version of the Shell Theorem analytical equations are derived to calculate the electric energy of a charged sphere and the field energy of the electrolyte inside and around the sphere. These electric energies are…
Using a proper gauge condition the static spherically symmetric solutions of Einstein-Maxwell equations with charged point source at the center are derived. It is shown that the solutions of the field equations are a three-parameter family…
Global topological defects described by real scalar field in (3,1) dimensions coupled to gravity are analyzed. We consider a class of scalar potentials with explicit dependence with distance, evading Derrick's theorem and leading to defects…
We study exact solutions of the Einstein-Maxwell equations for the interior gravitational field of static spherically symmetric charged compact spheres. The spheres are composed of a perfect fluid with a charge distribution that creates a…
We study configurations of points on the unit sphere that minimize potential energy for a broad class of potential functions (viewed as functions of the squared Euclidean distance between points). Call a configuration sharp if there are m…
Various solutions of the kinetic equation for the equilibrium of a gravitating sphere of uniform density with a quadratic gravitational potential and a linear dependence of gravitational force on radius are examined. New analytic solutions…
A new class of exact solutions of the Einstein-Maxwell system is found in closed form. This is achieved by choosing a generalised form for one of the gravitational potentials and a particular form for the electric field intensity. For…
We consider how the energy can be stored in the boundary of spacetime, in particular in a spherical bubble that can be made by a quantum gravitational process. Our calculation is performed within the framework of classical Einstein gravity…
The imposition of boundary conditions upon a quantized field can lead to singular energy densities on the boundary. We treat the boundaries as quantum mechanical objects with a nonzero position uncertainty, and show that the singular energy…
The effect of the uniform magnetic field on the electron in the spherically symmetric square-well potential is studied. A transcendental equation that determines the electron energy spectrum is derived. The approximate value of the lowest…
The exact solution for a static spherically symmetric field outside a charged point particle is found in a non-linear $U(1)$ gauge theory with a logarithmic Lagrangian. The electromagnetic self-mass is finite, and for a particular relation…
In this paper, we investigate discrete logarithmic energy problems in the unit circle. We study the equilibrium configuration of $n$ electrons and $n-1$ pairs of external protons of charge $+1/2$. It is shown that all the critical points of…
Global stability of the spherically symmetric nonisentropic compressible Euler equations with positive density around global-in-time background affine solutions is shown in the presence of free vacuum boundaries. Vacuum is achieved despite…
The quantum mechanical two-body problem with a central interaction on the sphere ${\bf S}^{n}$ is considered. Using recent results in representation theory an ordinary differential equation for some energy levels is found. For several…
Semiclassical approximation to the Wheeler-DeWitt equation which corresponds to gravity with a minimally coupled scalar field has been performed. To the leading order, vacuum Einstein's equation along with the functional Schrodinger…
According to Einstein's mass-energy equivalence, a body with a given mass extending in a large region of space, will get a smaller mass when confined into a smaller region, because of its own gravitational energy. The classical self-energy…