An exact solution of the metric-affine gauge theory with dilation, shear, and spin charges

TL;DR

This paper presents an exact static spherically symmetric vacuum solution in metric-affine gauge theory of gravity, incorporating nonmetricity and torsion, with matter sources including mass, dilation, shear, and spin charges.

Contribution

It provides the first exact solution describing the exterior of matter with dilation, shear, and spin charges in MAG, extending previous solutions.

Findings

Exact static spherically symmetric vacuum solution obtained

Includes effects of dilation, shear, and spin charges

Enhances understanding of MAG's geometric structures

Abstract

The spacetime of the metric-affine gauge theory of gravity (MAG) encompasses {\it nonmetricity} and {\it torsion} as post-Riemannian structures. The sources of MAG are the conserved currents of energy-momentum and dilation, shear and spin. We present an exact static spherically symmetric vacuum solution of the theory describing the exterior of a lump of matter carrying mass and dilation, shear and spin charges.