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

TL;DR

This work addresses the problem of modeling black holes in external electromagnetic fields within Einstein–Maxwell theory by constructing a new algebraic type D class with a non-aligned Faraday tensor relative to the Weyl tensor’s principal directions. The authors derive a rotating, twisting solution in Griffiths–Podolský form, parameterized by six physical quantities $m$, $a$, $l$, $α$, $c$, and $β$, and analyze two notable α=0 limits that yield Kerr-Newman-NUT and Kerr-Bertotti–Robinson spacetimes. The Kerr-Newman-NUT case reveals how charges and duality are encoded by $c$ and $β$, while the Kerr-BR limit demonstrates a black hole in a uniform magnetic field with rich horizon and geodesic structure. Overall, the paper expands the Plebański–Demiański family to non-aligned EM fields, includes known subcases, and provides a framework for exploring black holes in non-trivial EM backgrounds with potential astrophysical applications.

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 $α$, and parameter $β$ that governs the interplay between electric and magnetic charges in the aligned part of the Faraday tensor. This parameterization, as the Griffiths-Podolský form of the Plebański-Demiański 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.