Related papers: Axisymmetric solutions in the geomagnetic directio…
Magnetar magnetospheres gradually become twisted due to shearing by footpoint motion. The axisymmetric solutions for the force-free field with a power-law current model are calculated by taking into account general relativistic effects.…
It is known that there are nonlinear wave equations with localized solitary wave solutions. Some of these solitary waves are stable (with respect to a small perturbation of initial data) and have nonzero spin (nonzero intrinsic angular…
We establish sufficient conditions for existence of curves minimizing length as measured with respect to a degenerate metric on the plane while enclosing a specified amount of Euclidean area. Non-existence of minimizers can occur and…
We investigate how the azimuthal ambiguity in solar vector magnetogram data can be resolved by using the divergence-free property of magnetic fields. In a previous article, by Crouch, Barnes, and Leka (Solar Phys. 260, 271, 2009),…
The magnetic Dirichlet-to-Neumann map encodes the voltage-to-current measurements under the influence of a magnetic field. In the case of surfaces, we provide precise spectral asymptotics expansion (up to arbitrary polynomial power) for the…
The paper introduces a method to solve inverse problems for hyperbolic systems where the leading order terms are non-linear. We apply the method to the coupled Einstein-scalar field equations and study the question whether the structure of…
We consider the anisotropic Calderon problem of recovering a conductivity matrix or a Riemannian metric from electrical boundary measurements in three and higher dimensions. In the earlier work \cite{DKSaU}, it was shown that a metric in a…
This is the first in a series of two papers to establish the mass-angular momentum inequality for multiple black holes. We study singular harmonic maps from domains of 3-dimensional Euclidean space to the hyperbolic plane having bounded…
Non-relativistic conformally invariant systems in a rotating cosmic string (conical) spacetime are analyzed at the classical and quantum levels by means of the gravitoelectromagnetic interpretation of the background. Solutions of the…
We consider positive solutions to semilinear elliptic problems with singular nonlinearities, under zero Dirichlet boundary condition. We exploit a refined version of the moving plane method to prove symmetry and monotonicity properties of…
An existence result is shown for the asymptotic Dirichlet problem for harmonic maps from the product of the hyperbolic planes to the hyperbolic space, where the Dirichlet data is given on the distinguished boundary (the product of the…
We show that every entire solution to the Bernoulli (or one-phase) free boundary problem with finite Morse index in $\mathbb{R}^3$ is axially symmetric. In fact, we additionally prove that the same result would follow in any dimension $4…
Violation of the axial synnetry of a magnetic field essentially modifies the physics of the plasma outflow in the magnetosphere of rotating objects. In comparison to the axisymmetric outflow, two new affects appear: more efficient…
We study the problem of stationary bi-axially symmetric solutions of the $5$-dimensional minimal supergravity equations. Essentially all possible solutions with nondegenerate horizons are produced, having the allowed horizon cross-sectional…
We have constructed gravity solutions by breaking the Lorentzian symmetry to its subgroup, which means there is Galilean symmetry but without the rotational and boost invariance. This solution shows anisotropic behavior along both the…
It is shown that under essentially all conditions, the non-linear classical equations governing gravitation and matter in cosmology have a solution in which far outside the horizon in a suitable gauge the reduced spatial metric (the spatial…
In the framework of Einstein-Maxwell-axion theory we consider static spherically symmetric solutions, which describe a magnetic monopole in the axionic environment. These solutions are interpreted as the solutions for an axionic dyon, the…
It is found that the ideal magnetohydrodynamic equilibrium of an axisymmetric gravitating magnetically confined plasma with incompressible flows is governed by a second-order elliptic differential equation for the poloidal magnetic flux…
We present results from a numerical study of critical gravitational collapse of axisymmetric distributions of massless scalar field energy. We find threshold behavior that can be described by the spherically symmetric critical solution with…
From a purely none-general relativistic standpoint, we solve the empty space Poisson equation ($\nabla^{2}\Phi=0$) for an azimuthally symmetric setting, i.e., for a spinning gravitational system like the Sun. We seek the general solution of…