I have a question about connections derived from degenerate metrics, like in Newton-Cartan.(adsbygoogle = window.adsbygoogle || []).push({});

The question is simply: can the transformation properties of the connection change if one considers connections derived from metrics which are degenerate?

One one hand, I would say that one can follow the usual GR-analysis, check how covariant derivatives of general vectors/covectors must transform and conclude how the connection must transform (with a inhomogeneous term).

On the other hand, in Newton-Cartan one has the metric conditions

[tex]

\nabla_{\mu}\tau_{\nu} = 0, \ \ \ \ \nabla_{\rho}h^{\mu\nu}=0

[/tex]

where [itex]h^{\mu\nu}\tau_{\nu}=0[/itex]; h plays the role of spatial metric, and tau the role of temporal metric.

So, do the transformation properties of the connection depend on the metrical structure?

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# Connections of degenerate metrics

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