Energy conservation in GTR

The topics of gravitational field energy and energy-momentum conservation in General Relativity theory have been unjustly neglected by philosophers. If the gravitational field in space free of ordinary matter, as represented by the metric g ab itself, can be said to carry genuine energy and momentum, this is a powerful argument for adopting the substantivalist view of spacetime.This paper explores the standard textbook account of gravitational field energy and argues that (a) so-called stress-energy of the gravitational field is well-defined neither locally nor globally; and (b) there is no general principle of energy-momentum conservation to be found in General Relativity. I discuss the nature and justification of the zero-divergence law for ordinary stress-energy, and its possible connection with the failure of General Relativity to realise Mach's principle.
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    Alexander Afriat & Ermenegildo Caccese (2010). The Relativity of Inertia and Reality of Nothing. Studies in History and Philosophy of Science Part B 41 (1):9-26.
    Mathias Frisch (2009). Causality and Dispersion: A Reply to John Norton. British Journal for the Philosophy of Science 60 (3):487 - 495.
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