Certain Exact Solutions of the Equations of General Relativity with an Electrostatic Field

Abstract

Certain exact solutions of the field equations of general relativity for empty space containing an electrostatic field are derived, and a physical interpretation is attempted. The canonical cylinder coordinates of Weyl are used, and all the solutions in which the electrostatic potential depends on only one of the two variables are obtained. Some of these are special cases of a class of solutions previously obtained by Weyl and they are shown to correspond either to a uniform electric field or to the field of a line-charge. Two of the solutions are not members of Weyl's class, and in these the electric field has no analogue in classical electrostatics and possesses the property of generating an orthogonal gravitational field.