Einstein-Maxwell fields generated from the gamma-metric and their limits

TL;DR

This paper constructs new Einstein-Maxwell solutions from the gamma-metric using the Horsky-Mitskievitch conjecture, explores their limits, and verifies their properties through Ernst potentials and geodesic analysis.

Contribution

It introduces a method to generate Einstein-Maxwell fields from the gamma-metric and analyzes their limits and relations to known solutions.

Findings

Generated solutions reduce to the gamma-metric in vacuum limit

Some solutions correspond to known metrics

Limiting diagrams illustrate relations among solutions

Abstract

Two solutions of the coupled Einstein-Maxwell field equations are found by means of the Horsky-Mitskievitch generating conjecture. The vacuum limit of those obtained classes of spacetimes is the seed gamma-metric and each of the generated solutions is connected with one Killing vector of the seed spacetime. Some of the limiting cases of our solutions are identified with already known metrics, the relations among various limits are illustrated through a limiting diagram. We also verify our calculation through the Ernst potentials. The existence of circular geodesics is briefly discussed in the Appendix.