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Fantastic Beasts and where (not) to find them: Local gravitational energy and energy conservation in general relativity

2018; Elsevier BV; Volume: 65; Linguagem: Inglês

10.1016/j.shpsb.2018.07.002

1879-2502

Patrick M. Duerr,

Noncommutative and Quantum Gravity Theories

This paper critically examines energy-momentum conservation and local (differential) notions of gravitational energy in General Relativity (GR). On the one hand, I argue that energy-momentum of matter is indeed locally (differentially) conserved: Physical matter energy-momentum 4-currents possess no genuine sinks/sources. On the other hand, global (integral) energy-momentum conservation is contingent on spacetime symmetries. Local gravitational energy-momentum is found to be a supererogatory notion. Various explicit proposals for local gravitational energy-momentum are investigated and found wanting. Besides pseudotensors, the proposals considered include those of Lorentz and Levi-Civita, Pitts and Baker. It is concluded that the ontological commitment we ought to have towards gravitational energy in GR mimics the natural anti-realism/eliminativism towards apparent forces in Newtonian Mechanics.