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The classification of general affine connections in Newton–Cartan geometry: Towards metric-affine Newton–Cartan gravity

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Original languageEnglish
Article number015010
JournalClassical and Quantum Gravity
Volume42
Issue number1
Publication statusPublished - 12 Dec 2024

Abstract

We give a full classification of general affine connections on Galilei manifolds in terms of independently specifiable tensor fields. This generalises the well-known case of (torsional) Galilei connections, i.e. connections compatible with the metric structure of the Galilei manifold. Similarly to the well-known pseudo-Riemannian case, the additional freedom for connections that are not metric-compatible lies in the covariant derivatives of the two tensors defining the metric structure (the clock form and the space metric), which however are not fully independent of each other.

Keywords

    Newton–Cartan gravity, Galilei geometry, metric-affine geometry, metric-affine gravity, teleparallel gravity, symmetric teleparallel gravity

Cite this

The classification of general affine connections in Newton–Cartan geometry: Towards metric-affine Newton–Cartan gravity. / Schwartz, Philip K.
In: Classical and Quantum Gravity, Vol. 42, No. 1, 015010, 12.12.2024.

Research output: Contribution to journalArticleResearchpeer review

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KW - symmetric teleparallel gravity

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