Field Line Solutions of the Einstein-Maxwell Equations
arXiv:1911.04920
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 Rañada 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 Kopiński-Natário field which is discussed in some detail.
Published in An Essential Guide to Maxwell's Equations, Editor Casey Erickson, Nova Science Publishers, https://novapublishers.com/shop/an-essential-guide-to-maxwells-equations/