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Related Experiment Video

Updated: Jan 28, 2026

Fast Imaging Technique to Study Drop Impact Dynamics of Non-Newtonian Fluids
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Action Principle for Newtonian Gravity.

Dennis Hansen1, Jelle Hartong2, Niels A Obers3

  • 1Institut für Theoretische Physik, Eidgenössische Technische Hochschule Zürich Wolfgang-Pauli-Strasse 27, 8093 Zürich, Switzerland.

Physical Review Letters
|March 2, 2019
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Summary
This summary is machine-generated.

This study introduces a novel Newton-Cartan geometry to derive Newtonian gravity, extending it to include gravitational time dilation effects in strong fields.

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Area of Science:

  • Theoretical Physics
  • Gravitational Physics
  • Differential Geometry

Background:

  • Newtonian gravity is accurately described by the Poisson equation.
  • General relativity provides a more comprehensive theory of gravity.
  • A unified framework for Newtonian and relativistic gravity remains an area of research.

Purpose of the Study:

  • To derive an action for Newtonian gravity using a novel geometric approach.
  • To explore the connection between Newtonian gravity and general relativity via a covariant expansion.
  • To generalize Newtonian gravity by incorporating effects like gravitational time dilation.

Main Methods:

  • Development of a new Newton-Cartan geometry based on a distinct symmetry algebra.
  • Covariant 1/c expansion of general relativity, where c is the speed of light.
  • Truncation of the expansion at subleading order to identify field content and transformation rules.

Main Results:

  • Derivation of an action whose equations of motion yield the Poisson equation of Newtonian gravity.
  • Identification of a new Newton-Cartan geometry distinct from the Bargmann algebra.
  • Obtaining field content and transformation rules for Newtonian gravity fields from general relativity's expansion.

Conclusions:

  • The proposed framework naturally incorporates Newtonian gravity within a relativistic context.
  • The derived equations of motion generalize Newtonian gravity, accounting for gravitational time dilation.
  • This work offers a new geometric perspective on the relationship between Newtonian and relativistic gravity.