Comments on Maxwell's equations

Georgiou, A.

doi:10.1080/0020739820130106

Cited by 2 publications

(7 citation statements)

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“…are, respectively, the matter and electromagnetic stressenergy tensors and Instead of expressing the electromagnetic field equations in 4-dimensional form as in Equations (5), we shall use the Maxwell form (Maxwell's equations), because we can make direct comparisons with the results from classical electromagnetic theory. The electric and magnetic intensities and corresponding inductions in 3-vector form, are [4,5]…”

Section: The Einstein-maxwell Field Equationsmentioning

confidence: 99%

“…was set equal to in order to satisfy the continuity condition of 4 A Note that the full expression for r in the first of (28) is…”

Section: The Exterior Solutionmentioning

confidence: 99%

“…The discontinueties of these normal derivatives will generate a surface layer on with surface stress-energy tensor and surface 4-current and a more complicated set of junction conditions will apply. The Equations (12) and (13) for,   3 J and 4 J will give rise to expressions with factors of delta-functions and first order partial r-derivatives which are discontinuous on…”

Section:  mentioning

confidence: 99%

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A Global Solution of the Einstein-Maxwell Field Equations for Rotating Charged Matter

Georgiou¹

2012

JMP

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A stationary axially symmetric exterior electrovacuum solution of the Einstein-Maxwell field equations was obtained. An interior solution for rotating charged dust with vanishing Lorentz force was also obtained. The two spacetimes are separated by a boundary which is a surface layer with surface stress-energy tensor and surface electric 4-current. The layer is the spherical surface bounding the charged matter. It was further shown, that all the exterior physical quantities vanished at the asymptotic spatial infinity where spacetime was shown to be flat. There are two different sets of junction conditions: the electromagnetic junction conditions, which were expressed in the traditional 3-dimensional form of classical electromagnetic theory; and the considerably more complicated gravitational junction conditions. It was shown that both—the electromagnetic and gravitational junction conditions—were satisfied. The mass, charge and angular momentum were determined from the metric. Exact analytical formulae for the dipole moment and gyromagnetic ratio were also derived. The conditions, under which the latter formulae gave Blackett’s empirical result for rotating stars, were investigated

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Section: The Einstein-maxwell Field Equationsmentioning

confidence: 99%

“…was set equal to in order to satisfy the continuity condition of 4 A Note that the full expression for r in the first of (28) is…”

Section: The Exterior Solutionmentioning

confidence: 99%

Section:  mentioning

confidence: 99%

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A Global Solution of the Einstein-Maxwell Field Equations for Rotating Charged Matter

Georgiou¹

2012

JMP

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“…We have also shown that these equations are valid in all coordinate systems in flat and curved spaces [4]. Here we shall deal specifically with rotating coordinates.…”

Section: The Electromagnetic Field In Rotating Coordinatesmentioning

confidence: 99%

“…The electromagnetic field equations in vacuum electrodynamics expressed in tensor form are It may be shown [3], [4] that in any coordinate system in curved or flat spacetimes, (1) may be reduced to Maxwell's equations independent manner by use Cartesian forms for the divergence and curl operators. These are the reasons for the complicated form of their electromagnetic field equations in rotating coordinates.…”

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The electromagnetic field in rotating coordinates

Georgiou

1988

Proc. IEEE

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Please note that technical letters are no longer being considered for publication in the PROCEEDINGS OF THE IEEE. As announced in earlier issues, the letters Section will be discontinued in 1988. Letters already under review will be published upon acceptance as usual.Pages previously occupied by letters will gradually be used for papers to expand coverage. To that end, readers are encouraged to submit proposals for high-quality, general-interest papers, especially in areas less well covered in the past. For further information, see "Notice to Readers" in the July 1987 issue, page 868, and the boxed text on the second page of each issue of the PROCEEDINGS. The Electromagnetic Field in Rotating CoordinatesA. GEORGIOUThe electromagnetic field equations in rotating coordinates obtained by various authors, are based on incorrect expressions for the divergence and curl operators and the electromagnetic spatial vectors. This is a serious error in this most important aspect o f electromagnetic theory. Maxwell's equations are shown to be valid in rotating Coordinates.The problem of the electromagnetic field equations in rotating coordinates has been discussed in the literature by a number of authors. In particular, Schiff [I], and Atwater [2] obtained field equations which are extremely complicated and distinctly unlike Maxwell's equations. This i s a serious problem in electromagnetic theory, because it challenges the validity of Maxwell's equations in rotating Coordinates. We shall show that these treatments are faulty because they are based on incorrect expressions forthe electromagnetic 3-vectors and the 3-current and charge densities, as well as the divergence and curl operators.Shiozawa, (see remarks by T. Shiozawa in [2]), seems to have obtained Maxwell-like equations in rotating coordinates, but his treatment i s also based on incorrect expressions for the various quantities. The main source of error in all these treatments, is the failure to take account of the fact that the geometry of physical 3-space in rotating coordinates i s non-Euclidean.A treatment of Maxwell's equations in general coordinates was given by MQller [3]. We have also shown that these equations are valid in all coordinate systems in flat and curved spaces [4]. Here we shall deal specifically with rotating coordinates.We shall use theconvention in which Greek indices take thevalues 1,2,3,4for the spacetimecoordinates with x4 = t, Roman indices take the values 1,2, 3 for the space coordinates, the signature of the spacetime metric tensor g,, is +2, a comma denotes partial differentiation and we shall use M K S units. The electromagnetic field equations in vacuum electrodynamics expressed in tensor form arewhere F,. and Fp' = g""gU4Fmu are the covariant and contravariant electromagnetic tensors, i s the electric 4-current, po is the magnetic permeability of the vacuum, and g = lgpv1. We shall assume \-IWe note that the indices of spatial vectors are lowered and raised using the tensors y,, and y" respectively, and that the forms (covariant or ...

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Comments on Maxwell's equations

Cited by 2 publications

References 5 publications

A Global Solution of the Einstein-Maxwell Field Equations for Rotating Charged Matter

A Global Solution of the Einstein-Maxwell Field Equations for Rotating Charged Matter

The electromagnetic field in rotating coordinates

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