In theoretical general relativity, a geon is an electromagnetic or gravitational wave which is held together in a confined region by the gravitational attraction of its own field energy. They were first investigated theoretically in 1955 by J. A. Wheeler, who coined the term as a contraction of "gravitational electromagnetic entity."
Since general relativity is a classical field theory, Wheeler's concept of a geon does not treat them as quantum-mechanical entities, and this generally remains true today. Nonetheless, Wheeler speculated that there might be a relationship between microscopic geons and elementary particles. This idea continues to attract some attention among physicists, but in the absence of a viable theory of quantum gravity, the accuracy of this speculative idea cannot be tested. However recently Sundance Bilson-Thompson, Fotini Markopoulou, and Lee Smolin, in the context of Loop Quantum Gravity discovered some objects very similar to the Wheeler idea of geon.
Wheeler did not present explicit geon solutions to the vacuum Einstein field equation, a gap which was partially filled by Brill and Hartle in 1964 by the Brill-Hartle geon. This is an approximate solution which exhibits the features expected by Wheeler—at least temporarily. A major outstanding question regarding geons is whether they are stable, or must decay over time as the energy of the wave gradually "leaks" away. This question has not yet been definitively answered, but the consensus seems to be that they probably cannot be stable, which would lay to rest Wheeler's initial hope that a geon might serve as a classical model for stable elementary particles.
- Wheeler, J. A. (1957). "Geons". Physical Review 97 (2): 511. Bibcode:1955PhRv...97..511W. doi:10.1103/PhysRev.97.511.
- Brill, D. R.; Hartle, J. B. (1964). "Method of the Self-Consistent Field in General Relativity and its Application to the Gravitational Geon". Physical Review 135 (1B): B271. Bibcode:1964PhRv..135..271B. doi:10.1103/PhysRev.135.B271.
- Louko, Jorma; Mann, Robert B.; Marolf, Donald (2005). "Geons with spin and charge". Classical and Quantum Gravity 22 (7): 1451–1468. arXiv:gr-qc/0412012. Bibcode:2005CQGra..22.1451L. doi:10.1088/0264-9381/22/7/016.
- Perry, G. P.; Cooperstock, F. I. (1999). "Stability of Gravitational and Electromagnetic Geons". Classical and Quantum Gravity 16 (6): 1889–1916. arXiv:gr-qc/9810045. Bibcode:1999CQGra..16.1889P. doi:10.1088/0264-9381/16/6/321.
- Anderson, Paul R.; Brill, Dieter R. (1997). "Gravitational Geons Revisited". Physical Review D 56 (8): 4824–4833. arXiv:gr-qc/9610074. Bibcode:1997PhRvD..56.4824A. doi:10.1103/PhysRevD.56.4824.
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