Charging axisymmetric space-times with cosmological constant

TL;DR

This paper extends Ernst's solution generating technique to include the cosmological constant, enabling the generation of charged axisymmetric (A)dS black holes and a new magnetic universe solution.

Contribution

It generalizes Ernst equations for electromagnetic charge addition in axisymmetric spacetimes with a cosmological constant, linking them to a dual complex dynamical system.

Findings

Generated charged (A)dS black hole solutions from uncharged metrics.

Explicitly derived the Kerr-Newman-(A)dS metric from Kerr-(A)dS.

Produced a new magnetic universe solution with cosmological constant.

Abstract

Ernst's solution generating technique for adding electromagnetic charge to axisymmetric space-times in general relativity is generalised in presence of the cosmological constant. Ernst equations for complex potentials are found and they are traced back to an affective dual complex dynamical system, whose symmetries are studied. In particular this method is able to generate charged, asymptotically (A)dS black holes from their uncharged version: as an example, it is shown explicitly how to pass from the Kerr-(A)dS to the Kerr-Newman-(A)dS metric. A new solution describing a magnetic universe in presence of the cosmological constant is also generated.