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Action Principle for Newtonian Gravity

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arxiv 1807.04765 v3 pith:JGNLJM7Z submitted 2018-07-12 hep-th gr-qc

Dennis Hansen , Jelle Hartong , Niels A. Obers This is my paper
classification hep-thgr-qc
keywords gravitynewtonianactionalgebraequationsexpansionfieldsgeometry
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abstract

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.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Spin and Quadrupole Sectors in Nonrelativistic Gravity

    gr-qc 2026-05 unverdicted novelty 7.0 of 10

    Derives NLO Kerr-type and Hartle-Thorne-type solutions plus NNLO mixed spin-quadrupole solutions in the Galilean branch of nonrelativistic gravity.

  2. Stationary solutions in the small-$c$ expansion of GR

    gr-qc 2026-04 conditional novelty 7.0 of 10

    The NLO/NNLO small-c (Carroll) expansion of GR admits a rich stationary vacuum sector with rotating Lense-Thirring-type, C-metric-type, Hartle-Thorne-type, and higher-multipole solutions, going beyond the static magne...

  3. Stationary solutions in the small-$c$ expansion of GR

    gr-qc 2026-04 unverdicted novelty 6.0 of 10

    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.

  4. An Introduction to String Newton-Cartan Holography and Integrability

    hep-th 2026-03 accept novelty 3.0 of 10

    String Newton-Cartan holography, the non-relativistic limit of the AdS/CFT correspondence, is organized and reviewed around five consistency conditions, with its classical solutions, spectrum, and integrability structure.

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