Related papers: Heun-type solutions for Schwarzschild metric with …
Significant advances were made in recent years on the global evolution problem for self-gravitating massive matter in the small-perturbative regime close to Minkowski spacetime. To study the coupling between a Klein-Gordon equation and…
We report a solution of the one-dimensional Schrodinger equation with a hyperbolic double-well confining potential via a transformation to the so-called confluent Heun equation. We discuss the requirements on the parameters of the system in…
We study the competitive action of magnetic field, Coulomb repulsion and space curvature on the motion of a charged particle. The three types of interaction are characterized by three basic lengths: l_{B} the magnetic length, l_{0} the Bohr…
In this article we present a mechanism in which we find new non-perturbative solutions of quantum electrodynamics in four dimensions. Two non-perturbative solutions are found for approximate Schwinger-Dyson equations. The mass ratio of the…
In this paper we establish energy decay for solutions to the Klein-Gordon equation on the positive mass hyperboloidal anti-de Sitter Schwarzschild black hole, subject to Dirichlet, Neumann and Robin boundary conditions at infinity, for a…
We combine Maxwell's equations with Eulers's equation, related to a velocity field of an immaterial fluid, where the density of mass is replaced by a charge density. We come out with a differential system able to describe a relevant…
The ambiguity involved in the definition of effective-mass Hamiltonians for nonrelativistic models is resolved using the Dirac equation. The multistep approximation is extended for relativistic cases allowing the treatment of arbitrary…
We present, in an explicit form, the metric for all spherically symmetric Schwarzschild-Bach black holes in Einstein-Weyl theory. In addition to the black hole mass, this complete family of spacetimes involves a parameter that encodes the…
We consider the H\'enon problem \begin{equation*} \left\{ \begin{array} - - \Delta u = |x|^{\alpha} u^{\frac{N+2+2\alpha}{N-2}-\varepsilon} & \ \ \text{in} \ B_1, \\ u > 0 & \ \ \text{in} \ B_1, \\ u=0 & \ \ \text{on} \ \partial B_1,…
Static, spherically symmetric solutions of the Einstein--Kalb--Ramond (KR) field equations are obtained. Besides an earlier known exact solution, we also find an approximate, asymptotically flat solution for which the metric coefficients…
In this article are computed magnetic solutions of Einstein Maxwell Chern-Simons theory coupled to a dilaton-like scalar field. These solutions are computed by applying a space-time duality suggested by the author to known electric…
We show that mass parameter and radial coordinate values can be indirectly measured in thought experiments performed in Schwarzschild spacetime, without using the Newtonian limit of general relativity or approximations based on Euclidean…
We study the supersymmetry of the radial problems of the models of quantum relativistic rotating oscillators in arbitrary dimensions, defined as Klein-Gordon fields in backgrounds with deformed anti-de Sitter metrics. It is pointed out that…
Approximate analytical solutions of a two-term potential are studied for the relativistic wave equations, namely, for the Klein-Gordon and Dirac equations. The results are obtained by solving of a Riemann-type equation whose solution can be…
We consider radial solutions to the Cauchy problem for the linear wave equation with a small short-range electromagnetic potential (the "square version" of the massless Dirac equation with a potential) and zero initial data. We prove two a…
Dyonic and magnetic black holes solutions with spherically symmetric configurations in general relativity are obtained. Black holes possessing electric and magnetic charges are studied where the source of the gravitational field is…
We consider two-body problem in the self-field (1+1)-dimensional quantum electrodynamics on the circle. We present two formulations of the problem which correspond to two different types of variational principles and prove that both…
Based on the analogy with non-minimal SU(2) symmetric Wu-Yang monopole with regular metric, the solution describing a non-minimal U(1) symmetric Dirac monopole is obtained. In order to take into account the curvature coupling of…
In this paper, we study real solutions of the nonlinear Helmholtz equation $$ - \Delta u - k^2 u = f(x,u),\qquad x\in \R^N $$ satisfying the asymptotic conditions $$ u(x)=O(|x|^{\frac{1-N}{2}}) \quad \text{and} \quad \frac{\partial^2…
We study one of the interesting properties of the electromagnetic wave propagation in the curved Schwarzschild background spacetime in the framework of general relativity (GR). The electromagnetic wave equation has been derived from vacuum…