Example of a stable wormhole in general relativity

K.A. Bronnikov1, K.A. Bronnikov2, L.N. Lipatova, I.D. Novikov, A.A. Shatskiy3, I.D. Novikov4

Abstract

We study a static, spherically symmetric wormhole model whose metric coincides with that of the so-called Ellis wormhole but the material source of gravity consists of a perfect fluid with negative density and a source-free radial electric or magnetic field. For a certain class of fluid equations of state, it has been shown that this wormholemodel is linearly stable under both spherically symmetric perturbations and axial perturbations of arbitrary multipolarity. A similar behavior is predicted for polar nonspherical perturbations. It thus seems to be the first example of a stable wormhole model in the framework of general relativity (at least without invoking phantom thin shells as wormhole sources).

References

  1. C. Armendariz-Picon, Phys. Rev. D 65, 104010 (2002); gr-qc/0201027.
  2. H. Shinkai and S. A. Hayward, Phys. Rev. D 66, 044005 (2002); gr-qc/0205041.
  3. J. A. Gonzalez, F. S. Guzman, and O. Sarbach, Class. Quantum Grav. 26, 015010 (2009); ArXiv: 0806.0608.
  4. J. A. Gonzalez, F. S. Guzman, and O. Sarbach, Class. Quantum Grav. 26, 015011 (2009); ArXiv: 0806.1370.
  5. J. A. Gonzalez, F. S. Guzman, and O. Sarbach, Phys. Rev. D 80, 024023 (2009); ArXiv: 0906.0420.
  6. K. A. Bronnikov and S. Grinyok, Grav. Cosmol. 7, 297 (2001); gr-qc/0201083.
  7. K. A. Bronnikov and S. Grinyok, in: Inquiring the Universe, Festschrift in honor of Prof. Mario Novello, ed. by J. M. Salim et al. (Frontiers Group, 2003), p. 3353; gr-qc/0205131.
  8. A. Doroshkevich, J. Hansen, I. Novikov, and A. Shatskiy, Int. J. Mod. Phys. D 18, 1665 (2009); ArXiv: 0812.0702.
  9. I. D. Novikov, Astron. Reports 53(12), 1079 (2009).
  10. O. Sarbach and T. Zannias, Phys. Rev. D 81, 047502 (2010); ArXiv: 1001.1202.
  11. P. Kanti, B. Kleihaus, and J. Kunz, Phys. Rev. Lett. 107, 271101 (2011); ArXiv: 1108.3003.
  12. K. A. Bronnikov, Acta Phys. Pol. B 4, 251 (1973).
  13. H. G. Ellis, J.Math. Phys. 14, 104 (1973).
  14. M. S. Morris and K. S. Thorne, Am. J. Phys. 56, 395 (1988).
  15. K. A. Bronnikov, J. C. Fabris, and A. Zhidenko, EuroPhys J. C 71(11), 1791 (2011); ArXiv: 1109.6576.
  16. J. A. Wheeler, Phys. Rev. 97, 511 (1955).
  17. K. A. Bronnikov, V. N. Melnikov, G. N. Shikin, and K. P. Staniukovich, Ann. Phys. (N.Y.) 118, 84 (1979).
  18. I. D. Novikov and A. A. Shatskiy, JETP 114(5), 801 (2012); ArXiv: 1201.4112.
  19. S. Chandrasekhar, The Mathematical Theory of Black Holes (Clarendon, Oxford University Press, New York, 1983).
  20. A. A. Shatskii, I. D. Novikov, and N. S. Kardashev, Physics-Uspekhi 51, 457 (2008).
  21. K. A. Bronnikov, R. Konoplya, and A. Zhidenko, Phys. Rev. D 86, 024028 (2012); Arxiv: 1205.2224.
  22. V. Ferrari, M. Pauri, and F. Piazza, Phys. Rev. D 63, 064009 (2001); gr-qc/0005125.
For more information about this paper please visit Springer's Home Page of this paper.



Back to The Contents Page