An axially symmetric solution of metric-affine gravity

TL;DR

This paper introduces an exact axially symmetric vacuum solution in metric-affine gravity that extends previous spherically symmetric solutions, incorporating nonmetricity and torsion with physical parameters like mass, angular momentum, and charges.

Contribution

It provides the first known axially symmetric solution in MAG that includes nonmetricity and torsion, expanding the understanding of possible geometries in this theory.

Findings

Solution generalizes spherically symmetric cases

Parameters correspond to physical quantities like mass and spin

Includes nonmetricity and torsion in the metric framework

Abstract

We present an exact stationary {\it axially symmetric} vacuum solution of metric-affine gravity (MAG) which generalises the recently reported spherically symmetric solution. Besides the metric, it carries nonmetricity and torsion as post-Riemannian geometrical structures. The parameters of the solution are interpreted as mass and angular momentum and as dilation, shear and spin charges.