scholarly journals Magnetic fields in spaces with VII0 x VIII isometries.

2000 ◽  
Vol 53 (3) ◽  
pp. 345 ◽  
Author(s):  
Ciprian Dariescu ◽  
Marina-Aura Dariescu
Keyword(s):  
Magnetic Fields ◽  
Exact Solutions ◽  
Vector Potential ◽  
Maxwell Equations ◽  
Pathological Features ◽  
Penrose Diagram ◽  
Lorentz Condition

The aim of the present paper is to investigate some globally pathological features of a class of static planary symmetric exact solutions with a G6-group of motion, namely with g44 = –sinh2 (αz), by means of the null oblique geodesics and Penrose diagram. Finally, we derive general expressions for the Aµ(x, y, z)µ=1,3― components of the vector potential, satisfying the source-free Maxwell equations and the Lorentz condition, pointing out the influence of the global pathological properties on the behaviour of magnetostatic fields in such universes.

scholarly journals Soliton Model of the Photon / Fotona Solitona Modelis

2013 ◽  
Vol 50 (2) ◽  
pp. 60-67 ◽  
Author(s):  
I. Bersons
Keyword(s):  
Nonlinear Equation ◽  
Soliton Solution ◽  
Vector Potential ◽  
Maxwell Equations ◽  
Three Dimensional ◽  
Soliton Model ◽  
Dimensionless Constant ◽  
Dimensional Object ◽  
Dimensional Soliton ◽  
Wave Properties

A three-dimensional soliton model of photon with corpuscular and wave properties is proposed. We consider the Maxwell equations and assume that light induces the polarization and magnetization of vacuum only along the direction of its propagation. The nonlinear equation constructed for the vector potential is similar to the generalized nonlinear Schrödinger equation and comprises a dimensionless constant μ that determines the size-scale of soliton and is expected to be small. The obtained one-soliton solution of the proposed nonlinear equation describes a three-dimensional object identified as photon.

Classes of Exact Solutions of the Einstein-Maxwell Equations

1983 ◽  
Vol 495 (4-5) ◽  
pp. 181-188 ◽  
Author(s):  
V. G. Bagrov ◽  
V. V. Obukhov
Keyword(s):  
Exact Solutions ◽  
Maxwell Equations

scholarly journals Higher-derivative heterotic Double Field Theory and classical double copy

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Eric Lescano ◽  
Jesús A. Rodríguez
Keyword(s):  
Field Theory ◽  
Exact Solutions ◽  
Maxwell Equations ◽  
Action Principle ◽  
Low Energy ◽  
Gauge Fields ◽  
Metric Tensor ◽  
Higher Derivative ◽  
Double Field Theory ◽  
Double Copy

Abstract The generalized Kerr-Schild ansatz (GKSA) is a powerful tool for constructing exact solutions in Double Field Theory (DFT). In this paper we focus in the heterotic formulation of DFT, considering up to four-derivative terms in the action principle, while the field content is perturbed by the GKSA. We study the inclusion of the generalized version of the Green-Schwarz mechanism to this setup, in order to reproduce the low energy effective heterotic supergravity upon parametrization. This formalism reproduces higher-derivative heterotic background solutions where the metric tensor and Kalb-Ramond field are perturbed by a pair of null vectors. Next we study higher-derivative contributions to the classical double copy structure. After a suitable identification of the null vectors with a pair of U(1) gauge fields, the dynamics is given by a pair of Maxwell equations plus higher derivative corrections in agreement with the KLT relation.

Static magnetic fields in vacuum

2018 ◽  
Author(s):  
J. Pierrus
Keyword(s):  
Magnetic Field ◽  
Problem Solving ◽  
Magnetic Fields ◽  
Vector Potential ◽  
Scalar Potential ◽  
Multipole Expansion ◽  
Magnetic Vector Potential ◽  
Magnetic Dipoles ◽  
Static Magnetic Fields ◽  
The Magnetic Field

Wherever possible, an attempt has been made to structure this chapter along similar lines to Chapter 2 (its electrostatic counterpart). Maxwell’s magnetostatic equations are derived from Ampere’s experimental law of force. These results, along with the Biot–Savart law, are then used to determine the magnetic field B arising from various stationary current distributions. The magnetic vector potential A emerges naturally during our discussion, and it features prominently in questions throughout the remainder of this book. Also mentioned is the magnetic scalar potential. Although of lesser theoretical significance than the vector potential, the magnetic scalar potential can sometimes be an effective problem-solving device. Some examples of this are provided. This chapter concludes by making a multipole expansion of A and introducing the magnetic multipole moments of a bounded distribution of stationary currents. Several applications involving magnetic dipoles and magnetic quadrupoles are given.

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