Details
| Original language | English |
|---|---|
| Article number | 015010 |
| Journal | Classical and Quantum Gravity |
| Volume | 42 |
| Issue number | 1 |
| Publication status | Published - 3 Jan 2025 |
Abstract
Keywords
- Newton–Cartan gravity, Galilei geometry, metric-affine geometry, metric-affine gravity, teleparallel gravity, symmetric teleparallel gravity, Newton-Cartan gravity
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Physics and Astronomy (miscellaneous)
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In: Classical and Quantum Gravity, Vol. 42, No. 1, 015010, 03.01.2025.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The classification of general affine connections in Newton–Cartan geometry
T2 - Towards metric-affine Newton–Cartan gravity
AU - Schwartz, Philip K.
N1 - Publisher Copyright: © 2024 The Author(s). Published by IOP Publishing Ltd.
PY - 2025/1/3
Y1 - 2025/1/3
N2 - 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.
AB - 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.
KW - Newton–Cartan gravity
KW - Galilei geometry
KW - metric-affine geometry
KW - metric-affine gravity
KW - teleparallel gravity
KW - symmetric teleparallel gravity
KW - Newton-Cartan gravity
UR - http://www.scopus.com/inward/record.url?scp=85218760014&partnerID=8YFLogxK
U2 - 10.1088/1361-6382/ad922f
DO - 10.1088/1361-6382/ad922f
M3 - Article
VL - 42
JO - Classical and Quantum Gravity
JF - Classical and Quantum Gravity
SN - 0264-9381
IS - 1
M1 - 015010
ER -