The Teleparallel Equivalent of Newton-Cartan Gravity

Abstract

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.

arXiv comment7 pages, forthcoming in Classical and Quantum Gravity (letters)

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Cited by in corpus (12)

• Review on Non-Relativistic Gravity
• Teleparallel Newton--Cartan gravity
• The Non-Relativistic Geometric Trinity of Gravity
• Conformal Invariance of the Newtonian Weyl Tensor
• Underdetermination in Classic and Modern Tests of General Relativity
• New formulation of Galilean relativistic Maxwell theory
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• Is spacetime curved? Assessing the underdetermination of general relativity and teleparallel gravity
• Torsion in the Classical Spacetime Context
• Formulation of Galilean relativistic Born-Infeld theory
• Canonical Formulation for a Non-relativistic Spinning Particle Coupled to Gravity
• The Newtonian limit of orthonormal frames in metric theories of gravity