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Symmetry
Article . 2020 . Peer-reviewed
License: CC BY
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Symmetry
Article
License: CC BY
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https://dx.doi.org/10.48550/ar...
Article . 2019
License: arXiv Non-Exclusive Distribution
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Metric-Affine Geometries with Spherical Symmetry

Authors: Hohmann, Manuel;

Metric-Affine Geometries with Spherical Symmetry

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 SO ( 3 ) , which has been previously studied in the literature, and extend these previous results to the full orthogonal group O ( 3 ) , which also includes reflections. As an example for a potential physical application of the results we present here, we study circular orbits arising from autoparallel motion. Finally, we mention how these results can be extended to cosmological symmetry.

Related Organizations
Keywords

High Energy Physics - Theory, spacetime symmetry, High Energy Physics - Theory (hep-th), FOS: Physical sciences, metric-affine geometry, Mathematical Physics (math-ph), General Relativity and Quantum Cosmology (gr-qc), spherical symmetry, Mathematical Physics, General Relativity and Quantum Cosmology

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    51
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    Top 1%
    influence
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    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Top 10%
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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
51
Top 1%
Top 10%
Top 10%
Green
gold