Pleba\'nski-Demia\'nski-like solutions in metric-affine gravity

TL;DR

This paper explores a metric-affine gravity theory with nonmetricity and torsion, mapping solutions from Einstein-Maxwell theory, specifically the Plebański–Demiański class, to this non-Riemannian framework.

Contribution

It introduces a novel connection between Einstein-Maxwell solutions and a non-Riemannian metric-affine gravity theory, expanding the understanding of such solutions in alternative gravity models.

Findings

Mapped Plebański–Demiański solutions to metric-affine gravity

Established isomorphism between nonmetricity-torsion sector and Einstein–Maxwell theory

Demonstrated the applicability of Petrov type D metrics in this framework

Abstract

We consider a (non--Riemannian) metric--affine gravity theory, in particular its nonmetricity--torsion sector ``isomorphic'' to the Einstein--Maxwell theory. We map certain Einstein--Maxwell electrovacuum solutions to it, namely the Pleba\'nski--Demia\'nski class of Petrov type D metrics.