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Existence of oscillating solutions of Einstein $ {SU}(2)$ Yang-Mills equations


Author: Alexander N. Linden
Journal: Trans. Amer. Math. Soc. 359 (2007), 5125-5139
MSC (2000): Primary 83C20
DOI: https://doi.org/10.1090/S0002-9947-07-03402-2
Published electronically: June 4, 2007
MathSciNet review: 2327024
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Abstract | References | Similar Articles | Additional Information

Abstract: We give a rigorous proof that for small positive values of the cosmological constant the Einstein equations coupled to an SU(2) Yang-Mills connection yield oscillating spacetimes. These are static, spherically symmetric spacetimes that have the same topology as particle-like spacetimes but differ in geometry. We also give a strict upper bound on values of the cosmological constant that admit such spacetimes.


References [Enhancements On Off] (What's this?)

  • 1. R. Bartnik and J. McKinnon, Particlelike solutions of the Einstein-Yang-Mills equations, Physical Review Letters, 61 (2), 1988. MR 89e:83015
  • 2. R. Bartnik, The spherically symmetric Einstein Yang-Mills equations, Relativity Today--Proceedings of the third Hungarian Relativity Workshop, pages 221-240, 1989.
  • 3. P. Breitenlohner, P. Forgács, and D. Maison, Static spherically symmetric solutions of the Einstein-Yang-Mills equations, Communications in Mathematical Physics, 163 141-172, 1994. MR 95b:83021
  • 4. A. Linden, Existence of noncompact static spherically symmetric solutions of Einstein $ \operatorname{SU}(2)$-Yang-Mills equations, Communications in Mathematical Physics, 221 (3) 525-547, 2001. MR 2002f:53040
  • 5. A. Linden, Far field behavior of noncompact static spherically symmetric solutions of Einstein $ \operatorname{SU}(2)$-Yang-Mills equations, Journal of Mathematical Physics, 42 (3) 1196-1201, 2001. MR 2002d:53104
  • 6. A. Linden, Near field behavior of static spherically symmetric solutions of Einstein $ \operatorname{SU}(2)$-Yang-Mills equations with cosmological constant, Michigan Mathematics Journal, 50 (1) 201-224, 2002. MR 2003g:83021
  • 7. Alexander N. Linden, Horizons in spherically symmetric static Einstein 𝑆𝑈(2) Yang-Mills spacetimes, Classical Quantum Gravity 18 (2001), no. 4, 695–708. MR 1819857, https://doi.org/10.1088/0264-9381/18/4/309
  • 8. J. Smoller, A. Wasserman, S.-T. Yau, and J. B. McLeod, Smooth static solutions of the Einstein/Yang-Mills equations, Communications in Mathematical Physics, 143 115-147, 1991. MR 93a:58044
  • 9. J. Smoller and A. Wasserman, Existence of infinitely many smooth static solutions of the Einstein/Yang-Mills equations, Communications in Mathematical Physics, 151 (2) 303-325, 1993. MR 94a:58042
  • 10. J. Smoller and A. Wasserman, Regular solutions of the Einstein-Yang-Mills equations, Journal of Mathematical Physics, 36 (8), 4301-4323, August 1995. MR 96g:53037
  • 11. M. S. Volkov, N. Straumann, G. Lavrelashvili, M. Heusler, and O. Brodbeck, Cosmological analogues of the Bartnik-McKinnon solutions, Physical Reviews D, 54, 7243-7251, 1996.

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Additional Information

Alexander N. Linden
Affiliation: School of Mathematics and Statistics, University of Canberra, Australian Capital Territory #2601, Australia
Email: lindena_9@hotmail.com

DOI: https://doi.org/10.1090/S0002-9947-07-03402-2
Received by editor(s): July 27, 2001
Received by editor(s) in revised form: October 8, 2002
Published electronically: June 4, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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