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Action Principle for Newtonian Gravity
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Action Principle for Newtonian Gravity
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We derive an action whose equations of motion contain the Poisson equation of Newtonian gravity. The construction requires a new notion of Newton--Cartan geometry based on an underlying symmetry algebra that differs from the usual Bargmann algebra. This geometry naturally arises in a covariant $1/c$ expansion of general relativity with $c$ the speed of light. By truncating this expansion at subleading order we obtain the field content and transformation rules of the fields that appear in the action of Newtonian gravity. The equations of motion generalize Newtonian gravity by allowing for the effect of gravitational time dilation due to strong gravitational fields.
Forward citations
Cited by 2 Pith papers
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Spin and Quadrupole Sectors in Nonrelativistic Gravity
Derives NLO Kerr-type and Hartle-Thorne-type solutions plus NNLO mixed spin-quadrupole solutions in the Galilean branch of nonrelativistic gravity.
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Stationary solutions in the small-$c$ expansion of GR
Exact Lense-Thirring-type, C-metric-type, and Hartle-Thorne-type stationary vacuum solutions are constructed in the NLO and NNLO small-c expansion of GR, revealing a richer sector than magnetic Carroll gravity.
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