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arXiv · 2112.06503

Energy in Newtonian gravity

Ingemar Bengtsson·Tobias Eklund
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Abstract

In Newtonian gravity it is a moot question whether energy should be localized in the field or inside matter. An argument from relativity suggests a compromise in which the contribution from the field in vacuum is positive definite. We show that the same compromise is implied by Noether's theorem applied to a variational principle for perfect fluids, if we assume Dirichlet boundary conditions on the potential. We then analyse a thought experiment due to Bondi and McCrea that gives a clean example of inductive energy transfer by gravity. Some history of the problem is included

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Ingemar Bengtsson, Tobias Eklund. 2021-12-13. Energy in Newtonian gravity. https://doi.org/10.1007/s10701-022-00660-z

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