A novel class of rotating black holes with non-aligned electromagnetic field

TL;DR

This paper introduces a new class of rotating black hole solutions with non-aligned electromagnetic fields in Einstein-Maxwell theory, expanding the known solution space and providing a detailed parameterization for physical interpretation.

Contribution

The authors derive a novel algebraic type D solution with non-aligned electromagnetic fields, generalizing known black hole solutions and exploring its various forms and special cases.

Findings

New algebraic type D solution with non-aligned electromagnetic fields

Explicit parameterization including mass, charge, and rotation parameters

Reduction to known solutions in static limit

Abstract

We present a new class of expanding and twisting solutions to the Einstein-Maxwell equations of algebraic type D, where the null eigendirections of the Faraday tensor are not aligned with PNDs of the Weyl tensor. After deriving this novel solution, we explore its various metric forms and parameterizations. In suitable coordinates, the solution depends on six physical parameters, namely mass $m$, Kerr and NUT twist parameters $a$ and $l$, complex charge $c$, acceleration $\alpha$, and parameter $\beta$ that governs the interplay between electric and magnetic charges in the aligned part of the Faraday tensor. This parameterization, as the Griffiths-Podolsk\'{y} form of the Pleba\'{n}ski-Demia\'{n}ski solution, facilitates explicit special subcases, such as Kerr-Newman black holes, and a deeper physical interpretation. Additionally, in the static limit, our solution reduces to previously known cases.