arXiv research

Anisotropy of a space naturally leads to direction dependent electromagnetic tensors and electromagnetic potentials. Starting from this idea and using variational approaches and exterior derivative formalism, we extend some of the classical equations of electromagnetism to anisotropic (Finslerian) spaces. The results d…

Study examines wave equation decay and Strichartz estimates on conic manifolds.

New electromagnetic curvature defined via Jacobi-Maupertuis, showing positive curvature for non-zero magnetic force.

The paper construct a suitable generalized metrical multi-time Lagrange geometrical model for both gravitational and electromagnetic fields, in a general setting. In this construction, the gravitational potentials are described by a distinguished vertical metrical tensor of the form $h^{/alpha/beta}e^{2σ}/phi_{ij}$.

Nearly all field theories suffer from singularities when particles are introduced. This is true in both classical and quantum physics. Classical field singularities result in the notorious self-force problem, where it is unknown how the dynamics of a particle change when the particle interacts with its own (self) field…

Study magnetic perturbations in Riemannian and Lorentzian Calderón problems.

It is shown that Electromagnetism creates geometry different from Riemannian geometry. General geometry including Riemannian geometry as a special case is constructed. It is proven that the most simplest special case of General Geometry is geometry underlying Electromagnetism. Action for electromagnetic field and Maxwe…

In the present work, it is shown that, the application of the Bazanski approach to Lagrangians, written in AP-geometry and including the basic vector of the space, gives rise to a new class of path equations. The general equation representing this class contains four extra terms, whose vanishing reduces this equation t…

Physics-constrained neural nets solve EM fields of charged particle beams.

In the paper [4] is presented a theory which unifies the gravitation theory and the mechanical effects, which is different from the Riemannian theories like GTR. Moreover it is built in the style of the electomagnetic field theory. This paper is a continuation of [4] such that the complex variant of that theory yields …

Stable knots and links can exist in electromagnetic fields.

The paper introduces new geometric methods to analyze radar electromagnetic wave statistics.

Starting from a relativistic phenomenology of anyons in crystals, we discuss the concept of relativistic interaction and the need to unify electromagnetism and gravitation within the Spencer cohomology of Lie equations. Then, from the sophisticated non-linear Spencer complex of the Poincaré and conformal Lie pseudogrou…

The Dirichlet Laplacian between two parallel hypersurfaces in Euclidean spaces of any dimension in the presence of a magnetic field is considered in the limit when the distance between the hypersurfaces tends to zero. We show that the Laplacian converges in a norm-resolvent sense to a Schroedinger operator on the limit…

We present a gauge invariant generalization of Maxwell's equations and p-form electromagnetism to Kaehler spacetimes.

Closed and broken electromagnetic orbits in Kerr-Newman spacetime

In 2008-2009, F. Costa and C. Herdeiro proposed a new gravito-electromagnetic analogy, based on tidal tensors. We show that connections on the tangent bundle of the space-time manifold can help not only in finding a covnenient geometrization of their ideas, but also a common mathematical description of the main equatio…

Let X be a smooth manifold of dimension 1+n endowed with a lorentzian metric g, and let T be the electromagnetic energy tensor associated to a 2-form F. In this paper we characterize this tensor T as the only 2-covariant natural tensor associated to a lorentzian metric and a 2-form that is independent of the unit of sc…

Develops a Kaluza-Klein theory in affine spaces without metric.

Gravitational waves are predicted by the general theory of relativity. In [6] D. Christodoulou showed that gravitational waves have a nonlinear memory. We proved in [3] that the electromagnetic field contributes at highest order to the nonlinear memory effect of gravitational waves. In the present paper, we study this …

Algorithm finds real-analytic Legendrian representatives for every link type.

We discuss the coupling of the electromagnetic field with a curved and torsioned Lyra manifold using the Duffin-Kemmer-Petiau theory. We will show how to obtain the equations of motion and energy-momentum and spin density tensors by means of the Schwinger Variational Principle.

We prove boundedness and polynomial decay statements for solutions to the spin $\pm1$ Teukolsky-type equation projected to the $\ell=1$ spherical harmonic on Reissner-Nordström spacetime. The equation is verified by a gauge-invariant quantity which we identify and which involves the electromagnetic and curvature tensor…

We prove boundedness and polynomial decay statements for solutions to the spin $\pm2$ generalized Teukolsky system on a Reissner-Nordström background with small charge. The first equation of the system is the generalization of the standard Teukolsky equation in Schwarzschild for the extreme component of the curvature $…

In this paper a convergent series expansion is constructed to solve the prescribed mean curvature equation for n-dimensional hypersurfaces in n+1 dimensional Euclidean or Minkowskian space(time) which are graphs of a smooth real function u, and whose mean curvature function H is not too large in Hoelder norm, and integ…

We derive a system of equations governing the coupled gravitational and electromagnetic perturbations of Reissner-Nordström spacetime. The equations are derived in the context of global non-linear stability of Reissner-Nordström under axially symmetric polarized perturbations, as a generalization of the recent work on …

Study shows how electromagnetic and gravitational waves can form trapped surfaces.

A new model classifies lightning signals more accurately across different scales.

The aim of this paper is to construct a Riemann-Lagrange geometry on 1-jet spaces, in the sense of d-connections, d-torsions, d-curvatures, electromagnetic d-field and geometric electromagnetic Yang-Mills energy, starting from a given linear ODEs system or a given superior order ODE. The case of a non-homogenous linear…

New method finds precise late-time behavior of wave equations.

The paper deals with a formally self-adjoint first order linear differential operator acting on m-columns of complex-valued half-densities over an n-manifold without boundary. We study the distribution of eigenvalues in the elliptic setting and the propagator in the hyperbolic setting, deriving two-term asymptotic form…

By using variational calculus and exterior derivative formalism, we proposed in two previous joint papers with S. Siparov a new geometric approach for electromagnetism in pseudo-Finsler spaces. In the present paper, we provide more details, especially regarding generalized currents, the domain of integration and gauge …

We consider the Dirac equation in flat Minkowski 3-space and rewrite it as the Maxwell equation in Minkowski 4-space with torsion. The torsion tensor is defined as the dual of the electromagnetic vector potential. Our model clearly distinguishes the electron and the positron without resorting to "negative frequencies":…

Seminar held at JINR, Dubna, May 15, 2012. In General Relativity, spacetime singularities raise a number of problems, both mathematical and physical. One can identify a class of singularities - with smooth but degenerate metric - which, under a set of conditions, allow us to define proper geometric invariants, and to w…

For every link $L$ we construct a complex algebraic plane curve that intersects $S^3$ transversally in a link $\tilde{L}$ that contains $L$ as a sublink. This construction proves that every link $L$ is the sublink of a quasipositive link that is a satellite of the Hopf link. The explicit construction of the complex pla…

The aim of this paper is to construct a natural Riemann-Lagrange differential geometry on 1-jet spaces, in the sense of nonlinear connections, generalized Cartan connections, d-torsions, d-curvatures, jet electromagnetic fields and jet electromagnetic Yang-Mills energies, starting from some given nonlinear evolution OD…

Machine learning speeds up GPR simulations.

Paper develops a new method for solving IBVPs on star-shaped domains.

For a compact, connected, oriented Riemannian $3$-manifold $(M, g)$ with smooth boundary $\partial M$, we explicitly give a local representation and a full symbol expression for the electromagnetic Dirichlet-to-Neumann map by factorizing Maxwell's equations and using an isometric transform. We prove that one can recons…

In a previous paper on coupled gravitational and electromagnetic perturbations of Reissner-Nordström spacetime in a polarized setting, we derived a system of wave equations for two independent quantities, one related to the Weyl curvature and one related to the Ricci curvature of the perturbed spacetime. We analyze her…

FLASH-MAX predicts electromagnetic fields from sparse data in seconds.

We consider two areas of research that have been developing in parallel over the last decade: blind source separation (BSS) and electromagnetic source estimation (ESE). BSS deals with the recovery of source signals when only mixtures of signals can be obtained from an array of detectors and the only prior knowledge con…

In this paper we construct some natural geometrical objects on the 1-jet space J^1(R,R^3), like a nonlinear connection, a Cartan linear connection (together with its d-torsions and d-curvatures), a jet "electromagnetic" d-field and its geometric "electromagnetic" Yang-Mills energy, starting from a given dynamical syste…

In the framework of Galilei classical mechanics (i.e., general relativistic classical mechanics on a spacetime with absolute time) developed by Jadczyk and Modugno, we analyse systematically the relations between symmetries of the geometric objects. We show that the (holonomic) infinitesimal symmetries of the cosymplec…

We prove that for spacetimes solving the Einstein-Maxwell (EM) equations, the electromagnetic field contributes at highest order to the nonlinear memory effect of gravitational waves. In [5] D. Christodoulou showed that gravitational waves have a nonlinear memory. He discussed how this effect can be measured as a perma…

Classifies solutions in multisymplectic field theories using geometric gauge freedom.

Study on instability of extreme Reissner-Nordström spacetime perturbations.

In a previous paper, we have introduced a new unified description of the main equations of the gravitational and of the electromagnetic field, in terms of tidal tensors and connections on the tangent bundle TM of the space-time manifold. In the present work, we relate these equations to variational procedures on the ta…