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

Journal article

X. Bekaert, Kevin Morand
Journal of Mathematics and Physics, vol. 57(2), 2016, p. 022507

DOI: 10.1063/1.4937445

Cite

APA Click to copy
Bekaert, X., & Morand, K. (2016). Connections and dynamical trajectories in generalised Newton-Cartan gravity I. An intrinsic view. Journal of Mathematics and Physics, 57(2), 022507. https://doi.org/ 10.1063/1.4937445

Chicago/Turabian Click to copy
Bekaert, X., and Kevin Morand. “Connections and Dynamical Trajectories in Generalised Newton-Cartan Gravity I. An Intrinsic View.” Journal of Mathematics and Physics 57, no. 2 (2016): 022507.

MLA Click to copy
Bekaert, X., and Kevin Morand. “Connections and Dynamical Trajectories in Generalised Newton-Cartan Gravity I. An Intrinsic View.” Journal of Mathematics and Physics, vol. 57, no. 2, 2016, p. 022507, doi: 10.1063/1.4937445.

BibTeX Click to copy

@article{x2016a,
  title = {Connections and dynamical trajectories in generalised Newton-Cartan gravity I. An intrinsic view},
  year = {2016},
  issue = {2},
  journal = {Journal of Mathematics and Physics},
  pages = {022507},
  volume = {57},
  doi = {    10.1063/1.4937445},
  author = {Bekaert, X. and Morand, Kevin}
}

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 s...