Related papers: Magnetic flatness and E. Hopf's theorem for magnet…
By solving the Cauchy problem for the Hodge-Laplace heat equation for $d$-closed, positive $(1, 1)$-forms, we prove an optimal gap theorem for K\"ahler manifolds with nonnegative bisectional curvature which asserts that the manifold is flat…
In null electromagnetic fields the electric and the magnetic field lines evolve like unbreakable elastic filaments in a fluid flow. In particular, their topology is preserved for all time. We prove that for every link $L$ there is such an…
Let (A,m_A) -> (B,m_B) be a local morphism of local noetherian rings and M a finitely generated B-module. Then it follows from Tor^A_1(M,A/m_A) = 0 that M is a flat A-module. This is usually called the "local criterion of flatness". We give…
It is shown that all generalized two--dimensional dilaton theories with arbitrary matter content (with a curvature independent coupling to gravity) do not only obey a first law of black hole mechanics (which follows from Wald's general…
We give a mathematical exposition of the Page metric, and introduce an efficient coordinate system for it. We carefully examine the submanifolds of the underlying smooth manifold, and show that the Page metric does not have positive…
In this paper, we establish new geometric rigidity results through the study of Lyapunov exponent level sets via invariant measures. First, we prove that for a manifold $M$ without focal points, if the zero Lyapunov exponent level set has…
The motion of a charged particle moving on a flat surface is studied through the constants of motion associated to the system, given the magnetic gauge. The usual Landau' solution and the non separable solution for the Landau's gauge are…
This paper delves into the connection between flat and curvilinear magnetization dynamics. For this, we numerically study the evolution of the magnon spectrum of rectangular waveguides upon rolling its cross-section up to a full tube.…
In this paper, we formulate and prove a general compactness theorem for harmonic maps using Deligne-Mumford moduli space and families of curves. The main theorem shows that given a sequence of harmonic maps over a sequence of complex…
It is proved that any static system that is spacetime-geodesically complete at infinity, and whose spacelike-topology outside a compact set is that of R^3 minus a ball, is asymptotically flat. The matter is assumed compactly supported and…
We calculate exact one-dimensional collisionless plasma equilibria for a continuum of flux tube models, for which the total magnetic field is made up of the `force-free' Gold-Hoyle magnetic flux tube embedded in a uniform and anti-parallel…
We construct spherically symmetric and static solutions in $F(R)$ gravity coupled with electromagnetic fields. The solutions include new types of black holes with electric and magnetic charges. We show that the higher-derivative terms make…
We have solved the Einstein-Maxwell equations for a class of isotropic metrics with constant spatial curvature in the presence of magnetic fields. We consider a slight modification of the Tolman averaging relations so that the…
Recently, a geometric model for the confinement of magnetic charges in the context of type II string compactifications was constructed by Greene, Morrison and Vafa. This model assumes the existence of stable magnetic vortices with quantized…
As well known, magnetic fields in space are distributed very inhomogeneously. Some-times field distributions have forms of filaments with high magnetic field values. As many ob-servations show, such a filamentation takes place in convective…
To model magnetic fields of compact objects we solve the Maxwell equations in the background of the exterior static Schwarzschild and slowly rotating Kerr space-times. We impose the boundary condition that the electromagnetic fields are to…
Recent observational evidence that magnetic fields are dynamically important in molecular clouds, compared to self-gravity and turbulence, is reviewed and illustrated with data from the NGC 2024 region. One piece of evidence, turbulence…
In the large $U$ limit, the ground state of the half-filled, nearest-neighbor Hubbard model on the triangular lattice is the three-sublattice antiferromagnet. In sharp contrast with the square-lattice case, where transverse spin-waves and…
We study the Yang-Mills-Higgs system within the framework of general relativity. In the static situation, using Bogomol'nyi type analysis, we derive a positive-definite energy functional which has a lower bound. Specializing to the gauge…
We investigate the Einstein vacuum equations as well as the Einstein-null fluid equations describing neutrino radiation. We find new structures in gravitational waves and memory for asymptotically-flat spacetimes of slow decay. These…