Journal ArticleDOI
Static electromagnetic fields in general relativity: Part III
TLDR
In this article, the equations of the already unified theory for static electromagnetic fields were considered for the case in which the diagonalized metric tensor components are functions of two coordinates only, and the nonexistence of some types of solutions was demonstrated.About:
This article is published in Annals of Physics.The article was published on 1961-09-01. It has received 8 citations till now. The article focuses on the topics: Mathematics of general relativity & Classical electromagnetism and special relativity.read more
Citations
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Killing vector fields and the Einstein-Maxwell field equations in general relativity
H. Michalski,John Wainwright +1 more
Abstract: A number of theorems concerning non-null electrovac spacetimes, that is space-times whose metric satisfies the source-free Einstein-Maxwell equations for some non-null bivector Fij, are presented. Firstly, we suppose that the metric is invariant under a one-parameter group of isornetries with Killing vector field ξ. It is proved that the electromagnetic field tensor Fij is invariant under the group, in the sense that its Lie derivative with respect to ξ vanishes, if and only if the gradient αij of the complexion scalar is orthogonal to ξ. It is is also proved that if in addition ξ is hypersurface orthogonal, it is necessarily parallel to α,i. These results are used to generalize theorems of Perjes and Majumdar concerning static electrovac space-times. Secondly, we suppose that the metric is invariant under a two-parameter othogonally transitive Abelian group of isometries. It is proved that in this case Fij is necessarily invariant under the group. The above results can be used to simplify many derivations of exact solutions of the Einstein-Maxwell equations.
Journal ArticleDOI
Homogeneous nonstatic electromagnetic fields in general relativity
TL;DR: In this paper, two solutions of the Rainich equations for electromagnetic fields which are spatially homogeneous were presented, and it was shown that, except for some particular times when the field is entirely singular, there is a divergence-free electromagnetic field at all other times.
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On some Einstein-Maxwell fields of high symmetry
TL;DR: In this article, the authors considered static axisymmetric, stationary cylindrically symmetric and nonstatic spatially homogeneous space-times which were previously investigated in a series of papers by Raychaudhuri, Datta, Bera, and De.
Nonstatic electromagnetic fields in general relativity. ii.
K. Bera,B.K. Datta +1 more
Abstract: The Rainich equations of the `already unified field theory' are studied in the case of non-static electromagnetic fields, and a solution is obtained for a space-time metric which admits a group G4 of automorphisms. There exists a divergence-free electromagnetic field for x4 > 0, except for x4 -> infinity. It is shown that the electromagnetic field vanishes for large values of time, and the solution for a completely empty flat space is then obtained.
Journal ArticleDOI
Non-static electromagnetic fields in general relativity: II
TL;DR: In this article, the authors studied the Rainich equations of the already unified field theory in the case of non-static electromagnetic fields, and a solution was obtained for a space-time metric which admits a group G4 of automorphisms.
References
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Classical physics as geometry
TL;DR: In this paper, the electromagnetic field is given by the Maxwell square root of the contracted curvature tensor tensor of Ricci and Einstein, and a detailed description in terms of the existing beautiful and highly developed mathematics of topology and harmonic vector fields is traced out in detail.
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Electrodynamics in the general relativity theory
TL;DR: The electromagnetic tensor is, however, independent of the Riemann tensor in the ordinary genieral relativity theory; these two tenisors are connected by the so-called eniergy relation as discussed by the authors.
Journal ArticleDOI
Static electromagnetic fields in general relativity
TL;DR: In this article, the authors presented the solutions of the equations of Rainich's "already unified theory" for the case when the field is static and the diagonalized metric tensor components are functions of one coordinate alone.
Journal ArticleDOI
Static electromagnetic fields in general relativity
TL;DR: In this article, the equations of Rainich's "already unified theory" are solved for two simple types of static metrics, where the space-time admits of a group of motion whose minimum invariant varieties are two-dimensional spacelike surfaces of constant negative curvature.