HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

Connections and dynamical trajectories in generalised Newton-Cartan gravity I. An intrinsic view

Abstract : The "metric" structure of nonrelativistic spacetimes consists of a one-form (the absolute clock) whose kernel is endowed with a positive-definite metric. Contrarily to the relativistic case, the metric structure and the torsion do not determine a unique Galilean (i.e. compatible) connection. This subtlety is intimately related to the fact that the timelike part of the torsion is proportional to the exterior derivative of the absolute clock. When the latter is not closed, torsionfreeness and metric-compatibility are thus mutually exclusive. We will explore generalisations of Galilean connections along the two corresponding alternative roads in a series of papers. In the present one, we focus on compatible connections and investigate the equivalence problem (i.e. the search for the necessary data allowing to uniquely determine connections) in the torsionfree and torsional cases. More precisely, we characterise the affine structure of the spaces of such connections and display the associated model vector spaces. In contrast with the relativistic case, the metric structure does not single out a privileged origin for the space of metric-compatible connections. In our construction, the role of the Levi-Civita connection is played by a whole class of privileged origins, the so-called torsional Newton-Cartan (TNC) geometries recently investigated in the literature. Finally, we discuss a generalisation of Newtonian connections to the torsional case.
Document type :
Journal articles
Complete list of metadata

Contributor : Kevin Morand Connect in order to contact the contributor
Submitted on : Sunday, March 6, 2016 - 2:51:29 AM
Last modification on : Tuesday, January 11, 2022 - 5:56:09 PM

Links full text




Xavier Bekaert, Kevin Morand. Connections and dynamical trajectories in generalised Newton-Cartan gravity I. An intrinsic view. Journal of Mathematical Physics, American Institute of Physics (AIP), 2016, ⟨10.1063/1.4937445⟩. ⟨hal-01283693⟩



Record views