TY - JOUR

T1 - The classification of general affine connections in Newton–Cartan geometry

T2 - Towards metric-affine Newton–Cartan gravity

AU - Schwartz, Philip K.

PY - 2024/12/12

Y1 - 2024/12/12

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

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 -