The classification of general affine connections in Newton--Cartan geometry: Towards metric-affine Newton--Cartan gravity
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912717524172800 |
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| author | Schwartz, Philip K. |
| author_facet | Schwartz, Philip K. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15460 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The classification of general affine connections in Newton--Cartan geometry: Towards metric-affine Newton--Cartan gravity Schwartz, Philip K. Mathematical Physics General Relativity and Quantum Cosmology High Energy Physics - Theory Differential Geometry 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. |
| title | The classification of general affine connections in Newton--Cartan geometry: Towards metric-affine Newton--Cartan gravity |
| topic | Mathematical Physics General Relativity and Quantum Cosmology High Energy Physics - Theory Differential Geometry |
| url | https://arxiv.org/abs/2403.15460 |