Journal ArticleDOI
Static Magnetic Fields in General Relativity
W B Bonnor
- Vol. 67, Iss: 3, pp 225-232
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TLDR
In this paper, a class of known electrostatic solutions of the field equations to be adapted to the magnetostatic case was proved, and exact solutions referring to a uniform magnetic field and to a magnetic dipole were given.Abstract:
A theorem is proved which enables a class of known electrostatic solutions of the field equations to be adapted to the magnetostatic case. Exact solutions referring to a uniform magnetic field and to a magnetic dipole are given. The solution for a circular loop of wire carrying a steady current is considered, and it is shown that if the mass of the wire be neglected, both the magnetic and gravitational fields at great distances are equivalent to those of a magnetic dipole. The paper concludes with a short discussion of the significance of the solutions presented here, and in an earlier paper, for relativistic electromagnetic theory.read more
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Uniform Electromagnetic Field in the Theory of General Relativity
TL;DR: In this article, a cosmological solution of the Einstein-Maxwell's field equations, corresponding to the case of a uniform (that is, covariant constant) electromagnetic field, is derived by means of simple geometrical arguments; the Riemannian manifold it corresponds to is the product of two ordinary surfaces of constant curvature.
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A Class of Stationary Electromagnetic Vacuum Fields
Werner Israel,Gordon A. Wilson +1 more
TL;DR: In this paper, it was shown how a new class of stationary electromagnetic vacuum fields can be generated from solutions of Laplace's equation, which are a stationary generalization of the static electromagnetic vacuum field of Weyl, Majumdar, and Papapetrou, and are plausibly interpreted as exterior fields of static or steadily moving distributions of charged dust having numerically equal charge and mass densities.
Journal ArticleDOI
Kerr black holes in a magnetic universe
TL;DR: In this paper, exact expressions for the electromagnetic fields associated with arbitrarily charged Kerr-Newman black holes in a magnetic universe were presented. And for arbitrary charged black holes metrical corrections of order B0 are evaluated.
Journal ArticleDOI
Construction of exact solutions of the Einstein-Maxwell equations corresponding to a given behaviour of the Ernst potentials on the symmetry axis
V S Manko,N R Sibgatullin +1 more
TL;DR: In this article, a method developed by one of the authors for the construction of exact solutions of the Einstein-Maxwell equations by setting the behaviour of the Ernst potentials on the symmetry axis is discussed in full detail.
Journal ArticleDOI
On black holes in magnetic universes
TL;DR: In this paper, it was shown that no static magnetic universe Kerr-Newman black holes exist if either a, the Kerr angular momentum parameter, or e, the electric charge parameter, is nonzero.
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TL;DR: In this article, the tensor calculus and the law of gravitation have been studied in a tensor tensor geometry setting, and the authors present a review of the literature.
Journal ArticleDOI
A class of exact solutions of Einstein's field equations
TL;DR: In this paper, it was shown that the most general electrostatic field in which the two fields are functionally related can be represented by a line element of the form {(d{x}^{1})}^{2} = \ensuremath{-} 2log(1+v)$.
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Journal ArticleDOI
Certain Exact Solutions of the Equations of General Relativity with an Electrostatic Field
TL;DR: In this paper, the exact solutions of the field equations of general relativity for empty space containing an electrostatic field are derived, and a physical interpretation is attempted, and all the solutions in which the electrostatic potential depends on only one of the two variables are obtained.
Journal ArticleDOI
Integral electromagnetic theorems in general relativity
TL;DR: In this paper, it was shown that for an electromagnetic field in general relativity there exists a theorem which is expressed naturally in precisely the same form as the classical theorem of Gauss, but which admits a more general interpretation.