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arXiv · 1911.04920

Field Line Solutions of the Einstein-Maxwell Equations

Ion V. Vancea
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Abstract

In this paper, we are going to review the gravitating electromagnetic field in the 1+3 formalism on a general hyperbolic space-time manifold. We also discuss the recent results on the existence of the local field line solutions of the Einstein-Maxwell equations that generalize the Ra\~{n}ada solutions from the flat space-time. The global field line solutions do not always exist since the space-time manifold could impose obstructions to the global extension of various geometric objects necessary to build the fields. One example of a gravitating field line solution is the Kopi\'{n}ski-Nat\'{a}rio field which is discussed in some detail.

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Ion V. Vancea. 2019-11-11. Field Line Solutions of the Einstein-Maxwell Equations. https://arxiv.org/abs/1911.04920

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