Energy densities in Newtonian gravity from Maxwell, Bondi, and Ohanian have identical boundary behaviors and energy balances but are not equivalent, with Ohanian's distinguished on thermodynamic grounds.
The gravitational Poynting vector and energy transfer
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On the energy balance of Newtonian Gravitation
Energy densities in Newtonian gravity from Maxwell, Bondi, and Ohanian have identical boundary behaviors and energy balances but are not equivalent, with Ohanian's distinguished on thermodynamic grounds.