On the energy balance of Newtonian Gravitation

TL;DR

This paper compares different energy density formulas in Newtonian gravity, showing they share boundary conditions and energy balances but differ thermodynamically, highlighting the uniqueness of Ohanian's approach.

Contribution

It clarifies the distinctions among Newtonian gravity energy densities and emphasizes the thermodynamic significance of Ohanian's formulation.

Findings

Maxwell, Bondi, and Ohanian energy densities share boundary conditions.

Their energy balances are identical despite differences.

Ohanian's energy density is thermodynamically distinguished.

Abstract

It is shown that the energy density formulas of Newtonian gravity by Maxwell, Bondi and Ohanian cannot be distinguished by boundary conditions, and also the corresponding energy balances are identical. However, they are not equivalent. From a thermodynamic point of view, the Ohanian energy density is distinguished.