Energy in Newtonian gravity
arXiv:2112.06503 · doi:10.1007/s10701-022-00660-z
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
Version 2 has 18 pages, and was much improved by referees