Teleparallel Newton--Cartan gravity

Abstract

We discuss a teleparallel version of Newton--Cartan gravity. This theory arises as a formal large-speed-of-light limit of the teleparallel equivalent of general relativity (TEGR). Thus, it provides a geometric formulation of the Newtonian limit of TEGR, similar to standard Newton--Cartan gravity being the Newtonian limit of general relativity. We show how by a certain gauge-fixing the standard formulation of Newtonian gravity can be recovered.

arXiv comment28+4+1 pages (main text, references, appendix), published in Classical and Quantum Gravity. v2: extended discussions, added references, corrected typos. v3: corrected typo

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• Review on Non-Relativistic Gravity
• The Non-Relativistic Geometric Trinity of Gravity
• Geometric post-Newtonian description of massive spin-half particles in curved spacetime
• The classification of general affine connections in Newton--Cartan geometry: Towards metric-affine Newton--Cartan gravity
• Torsion in the Classical Spacetime Context
• From colored gravity to electromagnetism
• The Newtonian limit of orthonormal frames in metric theories of gravity
• On gauge transformations in twistless-torsional Newton--Cartan geometry
• Quantum interferometry in external gravitational fields