Multipole solutions in metric--affine gravity

TL;DR

This paper introduces a new class of multipole-like solutions within metric-affine gravity, a framework where nonmetricity, torsion, and curvature coexist, relevant for understanding spacetime at energies above the Planck scale.

Contribution

It presents the first application of the harmonic map ansatz to derive multipole solutions in metric-affine gravity, expanding the solution space of the theory.

Findings

New multipole-like solutions in MAG

Demonstrates the use of harmonic map ansatz in MAG

Enhances understanding of non-Riemannian geometries at high energies

Abstract

Above Planck energies, the spacetime might become non--Riemannian, as it is known fron string theory and inflation. Then geometries arise in which nonmetricity and torsion appear as field strengths, side by side with curvature. By gauging the affine group, a metric affine gauge theory emerges as dynamical framework. Here, by using the harmonic map ansatz, a new class of multipole like solutions in the metric affine gravity theory (MAG) is obtained.