The classification of general affine connections in Newton--Cartan geometry: Towards metric-affine Newton--Cartan gravity
arXiv:2403.15460 · doi:10.1088/1361-6382/ad922f
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.
arXiv comment20+2+2 pages (main text, references, appendix), to appear in Classical and Quantum Gravity. v2: added references, corrected typos. v3: extended discussion, added references
References in corpus (14)
- The teleparallel equivalent of general relativity
- Action Principle for Newtonian Gravity
- Non-Relativistic Gravity and its Coupling to Matter
- Torsional Newton-Cartan gravity from the large expansion of General Relativity
- Curved non-relativistic spacetimes, Newtonian gravitation and massive matter
- Connections and dynamical trajectories in generalised Newton-Cartan gravity I. An intrinsic view
- Review on Non-Relativistic Gravity
- Post-Newtonian extension of the Newton-Cartan theory
- The Teleparallel Equivalent of Newton-Cartan Gravity
- Covariant formulation of the post-1-Newtonian approximation to General Relativity
- Leibnizian, Galilean and Newtonian structures of spacetime
- Teleparallel Newton--Cartan gravity
- The Non-Relativistic Geometric Trinity of Gravity
- Generalized Newton-Cartan Geometries for Particles and Strings