Metric-affine Geometries With Spherical Symmetry
Manuel Hohmann

TL;DR
This paper classifies all spherically symmetric metric-affine geometries, including torsion, curvature, and nonmetricity, providing a foundation for solving gravity field equations with these geometries in various formulations.
Contribution
It offers a comprehensive classification of spherically symmetric metric-affine geometries, extending previous work to include reflections and analyzing their properties for gravity theories.
Findings
Classification of all subclasses based on geometric quantities
Extension from rotation group SO(3) to full O(3) including reflections
Application to autoparallel circular orbits
Abstract
We provide a comprehensive overview of metric-affine geometries with spherical symmetry, which may be used in order to solve the field equations for generic gravity theories which employ these geometries as their field variables. We discuss the most general class of such geometries, which we display both in the metric-Palatini formulation and in the tetrad / spin connection formulation, and show its characteristic properties: torsion, curvature and nonmetricity. We then use these properties to derive a classification of all possible subclasses of spherically symmetric metric-affine geometries, depending on which of the aforementioned quantities are vanishing or non-vanishing. We discuss both the cases of the pure rotation group , which has been previously studied in the literature, and extend these previous results to the full orthogonal group , which also…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
