Shear-free, twisting Einstein-Maxwell metrics in the Newman-Penrose formalism

Lind, Robert W.

doi:10.1007/bf00758073

Cited by 24 publications

(20 citation statements)

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“…It begins with the spin-coefficient version of the Maxwell equations in the coordinate and tetrad system associated with the shear-free twisting congruence. This has already been found and partially integrated [13,4]. Rather than repeat this calculation, we will simply quote the relevant parts.…”

Section: The Maxwell Fieldmentioning

confidence: 88%

“…The study of null geodesics and null geodesic congruences, in physical spacetime, has played a large role in many branches of mathematical physics, from the practical uses of the highfrequency limit of electromagnetic waves (leading to geometric optics and solutions of the eikonal equation) to the beautiful study of the special solutions of the Einstein equations (the so-called algebraically special vacuum metrics) which are determined by a special class of null geodesic congruences [1][2][3][4][5][6][7]. This work is devoted to a study of the physical meaning of this special class in the case of Minkowski space; a future work will be devoted to their meaning in curved spaces.…”

Section: Introductionmentioning

confidence: 99%

“…They could be either twisting [3,4] or non-twisting [1]. For many years these congruences were close to the centre of research activities in general relativity (GR).…”

Section: Introductionmentioning

confidence: 99%

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On Linear Topological Classification of Spaces of Continuous Functions in the Topology of Pointwise Convergence

Arkhangel’skiĭ¹

1991

Math. USSR Sb.

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We study and report on the class of vacuum Maxwell fields in Minkowski space that possess a non-degenerate, diverging, principal null vector field (null eigenvector field of the Maxwell tensor) that is tangent to a shear-free null geodesics congruence. These congruences can be either surface forming (the tangent vectors being proportional to gradients) or not, i.e., the twisting congruences. In the non-twisting case, the associated Maxwell fields are precisely the Lienard-Wiechert fields, i.e., those Maxwell fields arising from an electric monopole moving on an arbitrary worldline. The null geodesic congruence is given by the generators of the light-cones with apex on the worldline. The twisting case is much richer, more interesting and far more complicated.In a twisting subcase, where our main interests lie, the following strange interpretation can be given. If we allow the real Minkowski space to be complexified so that the real Minkowski coordinates x a take complex values, i.e., x a → z a = x a + iy a with complex metric g = η ab dz a dz b , the real vacuum Maxwell equations can be extended into the complex space and rewritten asThis subcase of Maxwell fields can then be extended into the complex space so as to have as source, a complex analytic worldline, i.e., to now become complex Lienard-Wiechart fields. When viewed as real fields on the real Minkowski space (z a = x a ), they possess a real principal null vector that is shear-free but twisting and diverging. The twist is a measure of how far the complex worldline is from the real 'slice'. Most Maxwell fields in this subcase are asymptotically flat with a time-varying set of electric and magnetic moments, all depending on the complex displacements and the complex velocities.

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Section: The Maxwell Fieldmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

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On Linear Topological Classification of Spaces of Continuous Functions in the Topology of Pointwise Convergence

Arkhangel’skiĭ¹

1991

Math. USSR Sb.

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“…1,2,3,4,5,6,7 This work is devoted to a study of the physical meaning of this special class in the case of Minkowski space; a future work will be devoted to their meaning in curved spaces. In the flat space case, the physical meaning or interpretation will come via certain associated Maxwell fields .…”

Section: Introductionmentioning

confidence: 99%

“…They could be either twisting 3,4 or non-twisting. 1 For many years these congruences were close to the center of research activities in GR.…”

Section: Introductionmentioning

confidence: 99%

Maxwell fields and shear-free null geodesic congruences

Newman¹

2004

Class. Quantum Grav.

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We study and report on the class of vacuum Maxwell fields in Minkowski space that possess a non-degenerate, diverging, principle null vector field (null eigenvector field of the Maxwell tensor) that is tangent to a shear-free null geodesics congruence. These congruences can be either surface forming (the tangent vectors being proportional to gradients) or not, i.e., the twisting congruences. In the non-twisting case, the associated Maxwell fields are precisely the Lienard-Wiechert fields, i.e., those Maxwell fields arising from

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The Newman-Penrose Method in the Theory of General Relativity

Frolov¹

1979

Problems in the General Theory of Relativity and Theory of Group Representations

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Shear-free, twisting Einstein-Maxwell metrics in the Newman-Penrose formalism

Cited by 24 publications

References 20 publications

On Linear Topological Classification of Spaces of Continuous Functions in the Topology of Pointwise Convergence

On Linear Topological Classification of Spaces of Continuous Functions in the Topology of Pointwise Convergence

Maxwell fields and shear-free null geodesic congruences

The Newman-Penrose Method in the Theory of General Relativity

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