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 THE MAXWELL LAGRANGIAN IN PURELY AFFINE GRAVITY

2008 ◽  
Vol 23 (03n04) ◽  
pp. 567-579 ◽  
Author(s):  
NIKODEM J. POPŁAWSKI
Keyword(s):  
Electromagnetic Field ◽  
Ricci Tensor ◽  
Maxwell Equations ◽  
Legendre Transformation ◽  
Conformal Transformations ◽  
Field Tensor ◽  
Metric Tensor ◽  
Hamiltonian Density ◽  
Electromagnetic Field Tensor ◽  
Affine Gravity

The purely affine Lagrangian for linear electrodynamics, that has the form of the Maxwell Lagrangian in which the metric tensor is replaced by the symmetrized Ricci tensor and the electromagnetic field tensor by the tensor of homothetic curvature, is dynamically equivalent to the Einstein–Maxwell equations in the metric–affine and metric formulation. We show that this equivalence is related to the invariance of the Maxwell Lagrangian under conformal transformations of the metric tensor. We also apply to a purely affine Lagrangian the Legendre transformation with respect to the tensor of homothetic curvature to show that the corresponding Legendre term and the new Hamiltonian density are related to the Maxwell–Palatini Lagrangian for the electromagnetic field. Therefore the purely affine picture, in addition to generating the gravitational Lagrangian that is linear in the curvature, justifies why the electromagnetic Lagrangian is quadratic in the electromagnetic field.

scholarly journals VARIATIONAL FORMULATION OF EISENHART'S UNIFIED THEORY

2009 ◽  
Vol 24 (20n21) ◽  
pp. 3975-3984
Author(s):  
NIKODEM J. POPŁAWSKI
Keyword(s):  
Variational Formulation ◽  
Ricci Tensor ◽  
Maxwell Equations ◽  
Affine Connection ◽  
Unified Theory ◽  
Field Tensor ◽  
Unified Field Theory ◽  
Field Equations ◽  
Unified Field ◽  
Electromagnetic Field Tensor

Eisenhart's classical unified field theory is based on a non-Riemannian affine connection related to the covariant derivative of the electromagnetic field tensor. The sourceless field equations of this theory arise from vanishing of the torsion trace and the symmetrized Ricci tensor. We formulate Eisenhart's theory from the metric-affine variational principle. In this formulation, a Lagrange multiplier constraining the torsion becomes the source for the Maxwell equations.

On a duality invariant action principle in vacuum electrodynamics

1970 ◽  
Vol 48 (20) ◽  
pp. 2423-2426 ◽  
Author(s):  
G. M. Levman
Keyword(s):  
Electromagnetic Field ◽  
Electromagnetic Fields ◽  
Maxwell Equations ◽  
Lagrangian Density ◽  
Vacuum Field ◽  
Field Tensor ◽  
Field Equations ◽  
Invariant Action ◽  
Electromagnetic Field Tensor ◽  
Derivatives Of

Although Maxwell's vacuum field equations are invariant under the so-called duality rotation, the usual Lagrangian density for the electromagnetic field, which is bilinear in the first derivatives of the electromagnetic potentials, does not exhibit that invariance. It is shown that if one takes the components of the electromagnetic field tensor as field variables then the most general Lorentz invariant Lagrangian density bilinear in the electromagnetic fields and their first derivatives is determined uniquely by the requirement of duality invariance. The ensuing field equations are identical with the iterated Maxwell equations.

scholarly journals Quantum electrodynamics with ∂ A μ /∂ x μ = 0

1946 ◽  
Vol 185 (1001) ◽  
pp. 192-206 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Quantum Electrodynamics ◽  
Maxwell Equations ◽  
Poisson Brackets ◽  
Relativistic Invariance ◽  
Field Equations ◽  
Vacuum Case ◽  
Commutation Relations ◽  
Longitudinal Part

The quantization of the electromagnetic field subject to ∂ A μ /∂ x μ = 0 ( A μ being the four-potential) developed in an earlier paper is reviewed, and a proof of the relativistic invariance of the commutation relations left out in the earlier paper supplied (§ 2). The Poisson brackets of A μ at two different points in space are worked out for the vacuum case (§ 3). If, instead of considering a field of matter, one considers explicitly different particles interacting with the electromagnetic field, such a theory gives us field equations which differ slightly from the equations of Dirac, Fock & Podolsky. By imposing a condition on Ψ occurring in nature, the Maxwell equations remain satisfied (§ 4, 5). Finally, it is shown how the equation ∂ A μ /∂ x μ = 0 can be brought into the new electrodynamics of Dirac and how, as a consequence, the longitudinal part of the field can be eliminated (§ 6).

scholarly journals Electromagnetic Field Equation and Lorentz Gauge in Rindler Space-time

2021 ◽  
Author(s):  
Sangwha Yi
Keyword(s):  
Electromagnetic Field ◽  
Gauge Transformation ◽  
Maxwell Equations ◽  
Space Time ◽  
Theory Of Relativity ◽  
Field Equations ◽  
Lorentz Gauge ◽  
Rindler Space ◽  
Differential Operation ◽  
Gauge Fixing

In this paper, we derived electromagnetic field transformations and electromagnetic field equations of Maxwell in Rindler space-time in the context of general theory of relativity. We then treat the Lorentz gauge transformation and the Lorentz gauge fixing condition in Rindler space-time and obtained the transformation of differential operation, the electromagnetic 4-vector potential and the field. In addition, charge density and the electric current density in Rindler spacetimeare derived. To view the invariance of the gauge transformation, gauge theory is applied to Maxwell equations in Rindler space-time. In Appendix A, we show that the electromagnetic wave function cannot exist in Rindler space-time. An important point we assert in this article is the uniqueness of the accelerated frame. It is because, in the accelerated frame, one can treat electromagnetic field equations.

Electromagnetic Field of Accelerated Charges in Inertial Frames with Substratum Flow

1990 ◽  
Vol 45 (5) ◽  
pp. 749-755
Author(s):  
H.E. Wilhelm
Keyword(s):  
Electromagnetic Field ◽  
Charged Particle ◽  
Maxwell Equations ◽  
Inertial Frame ◽  
Field Equations ◽  
Velocity Of Light ◽  
The Earth ◽  
Inertial Frames ◽  
Em Field

Abstract By means of the generalized Galilei covariant EM field equations, the EM potentials and EM fields of a charged particle moving with an arbitrary nonuniform velocity v(t) in an inertial frame with substratum flow w are calculated. It is shown that the dynamic EM fields are excitations of the EM ether caused by the motion v(t) - w of the charge relative to the wave carrier with velocity w. Qualitatively and quantitatively significant EM inductions and convective deformations of EM fields by the ether flow w exist in inertial frames with ether velocities w~c0 comparable to the velocity of light. For many terrestrial applications, the ordinary Maxwell equations agree in good approximation with the Galilei covariant EM field equations since w/c0~ 10-3 on the earth

Complexity factor for charged dissipative dynamical system

2020 ◽  
Vol 35 (28) ◽  
pp. 2050231
Author(s):  
M. Sharif ◽  
Saher Tariq
Keyword(s):  
Dynamical System ◽  
Electromagnetic Field ◽  
Maxwell Field ◽  
Anisotropic Fluid ◽  
Field Equations ◽  
Spherical System ◽  
Structure Scalars ◽  
Dissipative Dynamical System ◽  
The Stability ◽  
Dissipative Fluids

In this paper, we examine the complexity factor for a dynamical spherical system with dissipative charged anisotropic fluid. We evaluate the Einstein-Maxwell field equations and structure scalars using Bel’s approach which help to discuss the structure as well as evolution of a self-gravitating system. We measure the complexity factor for the pattern of evolution through the homologous condition and homogeneous expansion. We also analyze the stability of vanishing complexity condition for dissipative and non-dissipative fluids. It is found that the complexity as well as stability of the spherical system increases and decreases, respectively, under the effects of electromagnetic field.

scholarly journals HIGHER-ORDER CURVATURE TERMS IN BORN–INFELD TYPE BRANE THEORIES

2011 ◽  
Vol 20 (01) ◽  
pp. 59-75 ◽  
Author(s):  
EFRAIN ROJAS
Keyword(s):  
Ricci Tensor ◽  
General Structure ◽  
Extrinsic Curvature ◽  
Higher Order ◽  
Square Root ◽  
Auxiliary Variables ◽  
Field Equations ◽  
Alternative Description ◽  
Brane Models ◽  
Combined Matrix

The field equations associated to Born–Infeld type brane theories are studied by using auxiliary variables. This approach hinges on the fact, that the expressions defining the physical and geometrical quantities describing the worldvolume are varied independently. The general structure of the Born–Infeld type theories for branes contains the square root of a determinant of a combined matrix between the induced metric on the worldvolume swept out by the brane and a symmetric/antisymmetric tensor depending on gauge, matter or extrinsic curvature terms taking place on the worldvolume. The higher-order curvature terms appearing in the determinant form come to play in competition with other effective brane models. Additionally, we suggest a Born–Infeld–Einstein type action for branes where the higher-order curvature content is provided by the worldvolume Ricci tensor. This action provides an alternative description of the dynamics of braneworld scenarios.

SOLITARY WAVES OF THE NONLINEAR KLEIN-GORDON EQUATION COUPLED WITH THE MAXWELL EQUATIONS

2002 ◽  
Vol 14 (04) ◽  
pp. 409-420 ◽  
Author(s):  
VIERI BENCI ◽  
DONATO FORTUNATO FORTUNATO
Keyword(s):  
Electromagnetic Field ◽  
Solitary Wave ◽  
Electric Field ◽  
Solitary Waves ◽  
Maxwell Equations ◽  
Gordon Equation ◽  
Klein Gordon ◽  
Klein Gordon Equation

This paper is divided in two parts. In the first part we construct a model which describes solitary waves of the nonlinear Klein-Gordon equation interacting with the electromagnetic field. In the second part we study the electrostatic case. We prove the existence of infinitely many pairs (ψ, E), where ψ is a solitary wave for the nonlinear Klein-Gordon equation and E is the electric field related to ψ.

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