Energy in Newtonian gravity

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

arXiv commentVersion 2 has 18 pages, and was much improved by referees

References in corpus (6)

• Spectral Methods for Numerical Relativity
• On Gravitational Energy in Newtonian Theories
• The gauge invariance of general relativistic tidal heating
• The Mass of the Gravitational Field
• A note on the post-Newtonian limit of quasi-local energy expressions
• General Relativity's energy and positivity -- a brief history