Generalized static electromagnetic fields in relativity

Abstract

A general class of static cylindrically symmetric solutions of the Einstein-Maxwell equations coupled with a zero-rest-mass scalar field is obtained under the assumption -r 2grr = g00gφφgzz. These solutions reduce to Marder's well-known exterior solution in the absence of electromagnetic and scalar fields.

Cylindrical systems in general relativity

“…Here E and B are the absolute values of the electric field strength and magnetic induction, respectively. Selfgravitating static, cylindrically symmetric configurations of such electromagnetic fields have been considered in [62,63,238,272,301] ( in which see also references to earlier work, and more historical details can be found in [294]). In our presentation we follow the lines of [62,63].…”

Scalar Hairy Black Holes in the presence of Nonlinear Electrodynamics

“…This solution (2.27) corresponds to the one obtained in [20] only written in different notation for the constants. Also, using simple relations for hyperbolic functions that are used to write the solution in [22], one can show that our solution corresponds to theirs. Note that in [22], they obtained the solution representing pure magnetic field using the duality between electric and magnetic field.…”

“…Also, using simple relations for hyperbolic functions that are used to write the solution in [22], one can show that our solution corresponds to theirs. Note that in [22], they obtained the solution representing pure magnetic field using the duality between electric and magnetic field. As we will discuss subsequently, our solution has static vacuum solution limit.…”

“…Other branches of the Einstein-Maxwell scalar field solutions were later studied in [21]. Subsequent works [22] give a general class of static cylindrically symmetric solutions which allows combinations of electric and magnetic fields. The investigation proceeded to broaden the class of spacetimes even further and stationary axially symmetric Einstein-Maxwell scalar spacetimes were derived and a method to generate such solutions from the corresponding vacuum ones was presented [23].…”

The charged line-mass in general relativity

“…This solution has a long history [3][4][5][6][7][8][9][10], and several authors have reported unexpected features. Thus in [3] it was stated "No solution appears to exist for a line-charge with positive mass", and a similar conclusion appeared in [4,5]. Safko [7] concluded that in this solution there is no charge without mass, and Witten [6] wrote of the intimate connection of mass and charge in the general static cylindrical electromagnetic fields.…”