An investigation of axially symmetric electrovac solutions

Abstract

For the axially symmetric, electrostatic vacuum problem, there are three unknowns:g00,g11, and φ, the electrostatic field. Herlt, using his generation methods, has presented several new solutions by explicitly givingg00 andφ only. Theg11 is now determined in two cases and a detailed discussion of these solutions is given. The solutions do not, in general, possess the overlapping equipotential structure [g00=g00(φ)] which characterizes the Weyl class. One of the classes contains metrics which can be physically interpreted as representing exterior space-times of non-Weyl “two-body”-type charged “point” sources. With the specialization of the arbitrary parameters, the above solutions do reduce to known Weyl solutions. The Bonnor solution is a member of one of the above classes and consequently a possible physical reinterpretation of this solution is given. Kinnersley transformations applied to the above classes yield stationary space-times with line singularities and NUT-like asymptotic behavior.