Torsional Newton-Cartan gravity from the large $c$ expansion of General Relativity

Abstract

We revisit the manifestly covariant large $c$ expansion of General Relativity, $c$ being the speed of light. Assuming the relativistic connection has no pole in $c^{-2}$, this expansion is known to reproduce Newton-Cartan gravity and a covariant version of Post-Newtonian corrections to it. We show that relaxing this assumption leads to the inclusion of twistless torsion in the effective non-relativistic theory. We argue that the resulting TTNC theory is an effective description of a non-relativistic regime of General Relativity that extends Newtonian physics by including strong gravitational time dilation.

25 pages, v3 footnote on Kerr corrected, ref added

References in corpus (4)

• Newtonian Gravity and the Bargmann Algebra
• Carroll versus Galilei Gravity
• Torsional Newton-Cartan Geometry and the Schrödinger Algebra
• Torsional Newton-Cartan gravity and strong gravitational fields

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