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The Teleparallel Equivalent of Newton-Cartan Gravity

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arxiv 1807.11779 v1 pith:NNOV5ZZA submitted 2018-07-31 gr-qc

classification gr-qc
keywords teleparalleltheoryequivalentgravitynewton-cartangeneralnewtonianrelativity
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We construct a notion of teleparallelization for Newton-Cartan theory, and show that the teleparallel equivalent of this theory is Newtonian gravity; furthermore, we show that this result is consistent with teleparallelization in general relativity, and can be obtained by null-reducing the teleparallel equivalent of a five-dimensional gravitational wave solution. This work thus strengthens substantially the connections between four theories: Newton-Cartan theory, Newtonian gravitation theory, general relativity, and teleparallel gravity.

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    The authors classify general Carrollian affine connections with torsion and non-metricity, show their emergence from Lorentzian limits, and build an ultra-relativistic geometric trinity of gravity theories.

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