Related papers: Weighted energy problem on the unit sphere
We investigate the properties of $Q$-balls in $d$ spatial dimensions. First, a generalized virial relation for these objects is obtained. We then focus on potentials $V(\phi\phi^{\dagger})= \sum_{n=1}^{3} a_n(\phi\phi^{\dagger})^n$, where…
In this short note, we employ well-known results to improve the lower bound for the constant associated with the linear term in the asymptotic expansion of the minimal logarithmic energy on the sphere.
The Casimir-Polder and van der Waals interaction energy of an atom with infinitely thin sphere with finite conductivity is investigated in the framework of the hydrodynamic approach. We put the sphere into spherical cavity inside the…
A significantly lower upper limit to minimum energy solutions of the electrostatic Thomson Problem is reported. A point charge is introduced to the origin of each $N$-charge solution. This raises the total energy by $N$ as an upper limit to…
We discuss the weak-field limit of induced gravity and show that results directly depend on the coupling and self-interaction potential of the scalar field. A static spherically symmetric exact solution is found and its conformal properties…
We study a constrained minimum energy problem with an external field relative to the Riesz kernel of an arbitrary order for a generalized condenser with touching oppositely-charged plates. Conditions sufficient for the solvability of the…
We interpret the exact solutions previously obtained for spherically symmetric shells of liquid fluid in General Relativity in terms of the energies involved. We show that a certain parameter that was introduced into the solutions by the…
Minimum Riesz energy problems in the presence of an external field are analyzed for a condenser with touching plates. We obtain sufficient and/or necessary conditions for the solvability of these problems in both the unconstrained and the…
On the basis of obtained equations of the energy balance for scalar fields in cosmological models, a hypothesis formulated by the author on the existence of Euclidean limit cycles in cosmological models based on scalar fields with a Higgs…
We show improved local energy decay for the wave equation on asymptotically Euclidean manifolds in odd dimensions in the short range case. The precise decay rate depends on the decay of the metric towards the Euclidean metric. We also give…
We analyze an alternative theory of gravity characterized by metrics that are tensor density of rank(0,2)and weight-1/2.The metric compatibility condition is supposed to hold. The simplest expression for the action of gravitational field is…
We investigate spherically symmetric non topological solitons in electrodynamics with a scalar field self interaction U ~|\psi| taken from the complex signum-Gordon model. We find Q-balls for small absolute values of the total electric…
We study the exact solution of Einstein's field equations consisting of a ($n+2$)-dimensional static and hyperplane symmetric thick slice of matter, with constant and positive energy density $\rho$ and thickness $d$, surrounded by two…
The system of a proton and an electron in an inert and impenetrable spherical cavity is studied by solving Schr\"{o}dinger equation with the correct boundary conditions. The differential equation of a hydrogen atom in a cavity is derived.…
In relativity, the energy of a moving particle depends on the observer, and the rest mass is the minimal energy seen among all observers. The Wang-Yau quasi-local mass for a surface in spacetime introduced in [7] and [8] is defined by…
We consider some elementary features of Newtonian gravity, or electrostatics, as defined on an N-sphere. In particular, we present and discuss "the shell theorem" for this system.
In a previous paper, a bound on the negative energy density seen by an arbitrary inertial observer was derived for the free massless, quantized scalar field in four-dimensional Minkowski spacetime. This constraint has the form of an…
We study the restricted motion of an electric charge in a spherical surface in the field of a magnetic dipole. This is the classical non-relativistic St\"oermer problem within a sphere, with the dipole in its centre. We start from a…
Low-energy dynamics in the unit-charge sector of the CP^1 model on spherical space (space-time S^2 x R) is treated in the approximation of geodesic motion on the moduli space of static solutions, a six-dimensional manifold with non-trivial…
Motivated by recent works on the origin of inertial mass, we revisit the relationship between the mass of charged particles and zero-point electromagnetic fields. To this end we first introduce a simple model comprising a scalar field…