Fantastic Beasts and where (not) to find them: Local gravitational energy and energy conservation in general relativity |
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| Institution: | 1. Department of Collective Behaviour, Max Planck Institute of Animal Behavior, 78464 Konstanz, Germany;2. Department of Biology, University of Konstanz, 78464 Konstanz, Germany;3. Centre for the Advanced Study of Collective Behaviour, University of Konstanz, 78464 Konstanz, Germany;4. VERSES Research Labs, Los Angeles, CA, USA;5. Department of Mathematics, Imperial College London, London SW7 2AZ, UK;6. Wellcome Centre for Human Neuroimaging, University College London, London WC1N 3AR, UK;1. Departments of Mathematics, Physics and Astronomy, and Biomedical Engineering, Stony Brook University, Stony Brook, NY, 11794-3651, USA;2. VERSES Research Lab and Spatial Web Foundation, Los Angeles, CA, 90016, USA;1. BIASlab, Department of Electrical Engineering, Eindhoven University of Technology, Eindhoven, the Netherlands;2. VERSES Research Lab, Los Angeles, CA, 90016, USA;1. Department of Collective Behaviour, Max Planck Institute of Animal Behavior, 78464 Konstanz, Germany;2. Department of Biology, University of Konstanz, 78464 Konstanz, Germany;3. Centre for the Advanced Study of Collective Behaviour, University of Konstanz, 78464 Konstanz, Germany;4. VERSES Research Labs, Los Angeles, CA, USA;1. Department of Philosophy, University of Minnesota, Twin Cities, United States;2. Department of Logic and Philosophy of Science, University of California, Irvine, United States |
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| Abstract: | 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. |
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| Keywords: | Gravitational energy Energy conservation General relativity Inertial frames Pseudotensors Cosmological constant Energy-momentum tensor |
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