Generating Conjecture and Some Einstein-Maxwell Field of High Symmetry

TL;DR

This paper derives charged solutions to the Einstein-Maxwell equations with high symmetry using generating conjectures, connecting various known solutions through seed metrics and complex substitutions.

Contribution

It introduces a method to generate charged Einstein-Maxwell solutions from seed metrics, unifying several known solutions via the generating conjecture.

Findings

Charged solutions derived from seed metrics using generating conjecture.

Connections established between different solutions through complex substitutions.

Identification of seed metrics related to known Einstein-Maxwell solutions.

Abstract

For stationary cylindrically symmetric solutions of the Einstein-Maxwell equation we have shown that the "charged" solutions of McCrea, Chitre et al.(CGN), Van den Bergh and Wils (VW) can be obtained from the seed metrics using generating conjecture. The McCrea "charged" solution has as a seed vacuum metric the Van Stockum solution with a Killing vector (0,0,1,0). The CGN "charged" solution and the VW "charged" solution have the static seed metrics connected by the complex substitution (t --> iz), (z --> it) and the Killing vector which is a simple linear combination of ${\partial}_{\phi}$ and ${\partial}_{t}$ Killing vectors (VW), respectively ${\partial}_{\phi}$ and ${\partial}_{z}$ Killing vectors (CGN).