Pleba\'nski-Demia\'nski solutions with dynamical torsion and nonmetricity fields

TL;DR

This paper develops new stationary, axisymmetric solutions in Metric-Affine gravity incorporating dynamical torsion and nonmetricity, extending known metrics to include cosmological constant and additional physical charges.

Contribution

It introduces a class of Plebański-Demiański solutions with dynamical torsion and nonmetricity in Weyl-Cartan geometry, expanding the understanding of black hole configurations in Metric-Affine gravity.

Findings

Derived conditions for dynamical torsion and nonmetricity contributions.

Characterized black hole solutions with multiple physical charges.

Extended solutions to include cosmological constant and acceleration.

Abstract

We construct Pleba\'nski-Demia\'nski stationary and axisymmetric solutions with two expanding and double principal null directions in the framework of Metric-Affine gauge theory of gravity. Starting from the new improved form of the metric with vanishing cosmological constant recently achieved by Podolsk\'y and Vr\'atn\'y, we extend this form in the presence of a cosmological constant and derive the conditions under which the physical sources of the torsion and nonmetricity tensors provide dynamical contributions preserving it in Weyl-Cartan geometry. The resulting black hole configurations are characterised by the mass, orbital angular momentum, acceleration, NUT parameter, cosmological constant and electromagnetic charges of the Riemannian sector of the theory, as well as by the spin and dilation charges of the torsion and nonmetricity fields. The former is subject to a constraint representing a decoupling limit with the parameters responsible of axial symmetry, beyond which the geometry of the space-time is expected to be corrected.