Cooperstock's energy-localization hypothesis

In physics, the Cooperstock's energy-localization hypothesis is a hypothesis proposed by Fred Cooperstock that in general relativity, energy only exists in regions of non-vanishing energy–momentum tensor.[1]

Since the creation of general relativity there have been questions about the energy of gravitational fields. Among the proposals for the energy are the Landau–Lifshitz pseudotensor, Einstein pseudotensor, and the Møller superpotential.

In Misner, Thorne & Wheeler[2] the authors claimed that energy can only be localized for spherical systems, which Cooperstock & Sarracino [3] demonstrated implies that energy must be localized for all systems, while Bondi [4] argued that non-localizable energy is not allowed in general relativity.

The energy localization hypothesis has also been proven for a number of specific examples (see for example Ref [5][6]), but has not been proven or disproven in general.

Feynman's sticky bead argument shows that energy is transported by gravitational waves, which is difficult to make compatible with the Cooperstock's hypothesis.


  1. ^ F.I. Cooperstock, Found. Phys. 22, 1011 (1992)
  2. ^ Misner, Charles; Thorne, Kip S. & Wheeler, John Archibald (1973). Gravitation. San Francisco: W. H. Freeman. ISBN 0-7167-0344-0.
  3. ^ Cooperstock, F. I.; Sarracino, R. S. (1978). "The localisation of energy in general relativity". Journal of Physics A: Mathematical and General. IOP Publishing. 11 (5): 877–883. doi:10.1088/0305-4470/11/5/018. ISSN 0305-4470.
  4. ^ Bondi, H. (1990-02-08). "Conservation and Non-Conservation in General Relativity". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. The Royal Society. 427 (1873): 249–258. doi:10.1098/rspa.1990.0011. ISSN 1364-5021.
  5. ^ Xulu, S. S. (2000-08-10). "Møller Energy for the Kerr–Newman Metric". Modern Physics Letters A. World Scientific Pub Co Pte Lt. 15 (24): 1511–1517. arXiv:gr-qc/0010062. doi:10.1142/s0217732300001651. ISSN 0217-7323.
  6. ^ Xulu, S. S. (2000-12-10). "Energy Distribution in Melvin's Magnetic Universe". International Journal of Modern Physics A. World Scientific Pub Co Pte Lt. 15 (30): 4849–4856. arXiv:gr-qc/9912093. doi:10.1142/s0217751x00002007. ISSN 0217-751X.