scholarly journals The Proof that Maxwell Equations with the 3D E and B are not Covariant upon the Lorentz Transformations but upon the Standard Transformations: The New Lorentz Invariant Field Equations

2005 ◽  
Vol 35 (9) ◽  
pp. 1585-1615 ◽  
Author(s):  
Tomislav Ivezić
Keyword(s):  
Maxwell Equations ◽  
Lorentz Transformations ◽  
Field Equations

An analogy between electromagnetic and internal waves

2019 ◽  
Vol 485 (4) ◽  
pp. 428-433
Author(s):  
V. G. Baydulov ◽  
P. A. Lesovskiy
Keyword(s):  
Angular Momentum ◽  
Conservation Laws ◽  
Internal Wave ◽  
Special Relativity ◽  
Internal Waves ◽  
Maxwell Equations ◽  
Wave Equations ◽  
Lagrange Function ◽  
Lorentz Transformations ◽  
Symmetry Transformations

For the symmetry group of internal-wave equations, the mechanical content of invariants and symmetry transformations is determined. The performed comparison makes it possible to construct expressions for analogs of momentum, angular momentum, energy, Lorentz transformations, and other characteristics of special relativity and electro-dynamics. The expressions for the Lagrange function are defined, and the conservation laws are derived. An analogy is drawn both in the case of the absence of sources and currents in the Maxwell equations and in their presence.

scholarly journals GENERALIZED EINSTEIN–MAXWELL FIELD EQUATIONS IN THE PALATINI FORMALISM

2013 ◽  
Vol 22 (04) ◽  
pp. 1350017 ◽  
Author(s):  
GINÉS R. PÉREZ TERUEL
Keyword(s):  
Electromagnetic Field ◽  
Algebraic Equation ◽  
Ricci Tensor ◽  
Maxwell Equations ◽  
Natural Generalization ◽  
New Method ◽  
Maxwell Field ◽  
Field Equations ◽  
Palatini Formalism

We derive a new set of field equations within the framework of the Palatini formalism. These equations are a natural generalization of the Einstein–Maxwell equations which arise by adding a function [Formula: see text], with [Formula: see text] to the Palatini Lagrangian f(R, Q). The result we obtain can be viewed as the coupling of gravity with a nonlinear extension of the electromagnetic field. In addition, a new method is introduced to solve the algebraic equation associated to the Ricci tensor.

scholarly journals Exact Axially Symmetric Solution inf(T)Gravity Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Gamal G. L. Nashed
Keyword(s):  
Vacuum Solution ◽  
Gravity Theory ◽  
Kerr Metric ◽  
Radial Coordinate ◽  
Lorentz Transformations ◽  
Axially Symmetric ◽  
Field Equations ◽  
Tetrad Field ◽  
Kerr Spacetime ◽  
Euler’S Angles

A general tetrad field with sixteen unknown functions is applied to the field equations off(T)gravity theory. An analytic vacuum solution is derived with two constants of integration and an angleΦthat depends on the angle coordinateϕand radial coordinater. The tetrad field of this solution is axially symmetric and the scalar torsion vanishes. We calculate the associated metric of the derived solution and show that it represents Kerr spacetime. Finally, we show that the derived solution can be described by two local Lorentz transformations in addition to a tetrad field that is the square root of the Kerr metric. One of these local Lorentz transformations is a special case of Euler’s angles and the other represents a boost when the rotation parameter vanishes.

A study on charged compact stars

2019 ◽  
Vol 28 (03) ◽  
pp. 1950053 ◽  
Author(s):  
S. K. Maurya ◽  
Saibal Ray ◽  
Abdul Aziz ◽  
M. Khlopov ◽  
P. Chardonnet
Keyword(s):  
Maxwell Equations ◽  
Stellar System ◽  
Compact Stars ◽  
Physical Analysis ◽  
Field Equations ◽  
Electromagnetic Mass ◽  
Regular Solutions ◽  
Mass Model ◽  
Class 1 ◽  
Physical Features

In this paper, the Einstein–Maxwell spacetime is considered for compact stellar system. To find out solutions of the field equations, we adopt a finite and positive well-behaved metric potential. Under this particular choice, we therefore develop the expressions of the physical features, such as mass, charge, density and pressure, for stellar system in embedding class 1 spacetime. It is observed that all these features are physically viable. In the model, some known compact stars, viz. [Formula: see text] 1820–30, [Formula: see text] 1608–52 and [Formula: see text] 1745–248 [Formula: see text] are studied successfully through physical analysis. It is also interesting to note that the obtained set of regular solutions to the Einstein–Maxwell equations represents an electromagnetic mass model for isotropic fluid without invoking any negative pressure.

Exact solutions of the Einstein–Maxwell equations with linear equation of state

2012 ◽  
Vol 90 (12) ◽  
pp. 1179-1183 ◽  
Author(s):  
Tooba Feroze
Keyword(s):  
Equation Of State ◽  
Linear Equation ◽  
Maxwell Equations ◽  
Momentum Conservation ◽  
Conservation Equation ◽  
Fluid Distribution ◽  
Spherically Symmetric ◽  
Field Equations ◽  
General Linear Equation ◽  
Energy Momentum Conservation

Two new classes of solutions of the Einstein–Maxwell field equations are obtained by substituting a general linear equation of state into the energy–momentum conservation equation. We have considered static, anisotropic, and spherically symmetric charged perfect fluid distribution of matter with a particular form of gravitational potential. Expressions for the mass–radius ratio, the surface, and the central red shift horizons are given for these solutions.

Kerr–Newman solution in modified teleparallel theory of gravity

2014 ◽  
Vol 24 (01) ◽  
pp. 1550007 ◽  
Author(s):  
Gamal G. L. Nashed
Keyword(s):  
Azimuthal Angle ◽  
Polar Angle ◽  
Radial Coordinate ◽  
Lorentz Transformations ◽  
Square Root ◽  
Axially Symmetric ◽  
Field Equations ◽  
Tetrad Field ◽  
Teleparallel Theory ◽  
Theory Of Gravity

A nondiagonal tetrad field having six unknown functions plus an angle Φ, which is a function of the radial coordinate r, azimuthal angle θ and the polar angle ϕ, is applied to the charged field equations of modified teleparallel theory of gravity. A special nonvacuum solution is derived with three constants of integration. The tetrad field of this solution is axially symmetric and its scalar torsion is constant. The associated metric of the derived solution gives Kerr–Newman spacetime. We have shown that the derived solution can be described by a local Lorentz transformations plus a diagonal tetrad field that is the square root of the Kerr–Newman metric. We show that any solution of general relativity (GR) can be a solution in f(T) under certain conditions.

A Semi-Implicit Scheme for Modeling the Interaction Between Biological Cells and Electric Fields

2007 ◽  
Author(s):  
John H. Pierse ◽  
Arturo Ferna´ndez
Keyword(s):  
Fluid Flow ◽  
Electric Field ◽  
Maxwell Equations ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Computational Time ◽  
Biological Cells ◽  
Field Equations ◽  
Flow Equations

A numerical method for computing the simultaneous solution to the fluid flow equations and the electrostatic field equations is described. The methodology focuses on the modeling of biological cells suspended in fluid plasma. The fluid flow is described using the Navier-Stokes equations for incompressible flows. The electric field is computed trough the Maxwell equations neglecting magnetic effects. The effect of the electric field on the fluid flow is accounted for through the Maxwell stresses. The systems are described by a set of partial differential equations where the solution requires the simultaneous computation of the velocity, pressure and electric potential fields. A semi-implicit numerical scheme is proposed. In order to decrease the computational time required, it is proposed to use a semi-implicit splitting scheme where the Navier-Stokes and Maxwell equations are solved sequentially. The method is used to reproduce the response of human leukocytes immersed in a rotating electric field. An agreement between the numerical results and the data from experiments is observed.

Sedenionic formulation for the field equations of multifluid plasma

2020 ◽  
pp. 2150040
Author(s):  
Süleyman Demir ◽  
Damla Sümer ◽  
Murat Tanışlı
Keyword(s):  
Fluid Dynamics ◽  
Wave Equation ◽  
Maxwell Equations ◽  
Mathematical Tool ◽  
Source Terms ◽  
Classical Electromagnetism ◽  
Field Equations ◽  
Multifluid Plasma

In this paper, the multifluid equations of a plasma are reformulated in terms of conic sedenions in order to better reflect the analogies between multifluid plasma equations and Maxwell equations of classical electromagnetism. This formalism also provides us an efficient mathematical tool for unification of equations of fluid dynamics and electromagnetism in a compact and elegant way. Although the presented formulation enables us to express all of the field equations related to different disciplines, a set of Maxwell equations for multifluid plasma is combined into a single sedenionic equation. Moreover, the wave equation with source terms is generalized in a form similar to gravi-electromagnetism counterpart previously derived using this type sedenion.

scholarly journals Quaternionic Approach to Dual Magnetohydrodynamics of Dyonic Cold Plasma

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
B. C. Chanyal ◽  
Mayank Pathak
Keyword(s):  
Wave Equation ◽  
Cold Plasma ◽  
Maxwell Equations ◽  
Magnetic Monopoles ◽  
Alfven Wave ◽  
Vorticity Field ◽  
Field Equations ◽  
Continuity Equations ◽  
Fields Equations ◽  
Quaternionic Formulation

The dual magnetohydrodynamics of dyonic plasma describes the study of electrodynamics equations along with the transport equations in the presence of electrons and magnetic monopoles. In this paper, we formulate the quaternionic dual fields equations, namely, the hydroelectric and hydromagnetic fields equations which are an analogous to the generalized Lamb vector field and vorticity field equations of dyonic cold plasma fluid. Further, we derive the quaternionic Dirac-Maxwell equations for dual magnetohydrodynamics of dyonic cold plasma. We also obtain the quaternionic dual continuity equations that describe the transport of dyonic fluid. Finally, we establish an analogy of Alfven wave equation which may generate from the flow of magnetic monopoles in the dyonic field of cold plasma. The present quaternionic formulation for dyonic cold plasma is well invariant under the duality, Lorentz, and CPT transformations.

A new approach on electromagnetism with dual number coefficient octonion algebra

2016 ◽  
Vol 13 (09) ◽  
pp. 1630013 ◽  
Author(s):  
Bhupesh Chandra Chanyal ◽  
Sunil Kumar Chanyal ◽  
Özcan Bektaş ◽  
Salim Yüce
Keyword(s):  
Maxwell Equations ◽  
Wave Equations ◽  
Space Time ◽  
Internal Space ◽  
Field Equations ◽  
Octonion Algebra ◽  
New Approach ◽  
Dual Number ◽  
Symmetrical Form ◽  
Unit Formula

Dual number coefficient octonion (DNCO) is one of the kind of octonion, it has 16 components with an additional dual unit [Formula: see text]. Starting with DNCO algebra, we develop the generalized electromagnetic field equations of dyons regarding the DNCOS spaces, which has two octonionic space-times namely the octonionic internal space-time and the octonionic external space-time. Besides, the generalized four-potential components of dyons have been expressed with respect to the dual octonion form. Furthermore, we obtain the symmetrical form of Dirac–Maxwell equations, and the generalized potential wave equations for dyons in terms of the dual octonion. Finally, we conclude that dual octonion formulation is compact and simpler like octonion formulation.

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