Gravitation and Cosmology

, Volume 25, Issue 1, pp 44–49 | Cite as

On Gravitational Lensing by Symmetric and Asymmetric Wormholes

  • K. A. BronnikovEmail author
  • K. A. Baleevskikh


We discuss the peculiarities of gravitational lensing by spherically symmetric wormholes if they are not symmetric with respect to their throats. It is noticed, in particular, that wormholes always contain the so-called photon spheres, near which the photon deflection angles can be arbitrarily large, but, in general, the throat is such a sphere only for symmetric wormholes. In some cases, photons from outside can cross the throat and return back from a neighborhood of a photon sphere if the latter is located beyond the throat. Two families of generally asymmetric wormhole configurations are considered as examples: (1) anti-Fisher wormholes with a massless phantom scalar field as a source of gravity, and (2) wormholes with a zero Ricci scalar that may be interpreted as vacuum configurations in a brane world. The photon effective potentials and deflection angles for them are found and discussed.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    C. M. Will, “The confrontation between general relativity and experiment”, Living Rev. Rel. 17, 4 (2014); arXiv: 1403. 7377.CrossRefzbMATHGoogle Scholar
  2. 2.
    Hideki Asada, “Gravitational lensing by exotic objects,” Mod. Phys. Lett. A 32, 1730031 (2017); arXiv: 1711. 01730.ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Naoki Tsukamoto, “Deflection angle in the strong deflection limit in a general asymptotically flat, static, spherically symmetric spacetime,” Phys. Rev. D 95, 064035 (2017); arXiv: 1612. 08251.ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    O. Bergmann and R. Leipnik, “Space-time structure of a static spherically symmetric scalar field,” Phys. Rev. 107, 1157 (1957).ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    Homer G. Ellis, “Ether flow through a drainhole: A particle model in general relativity,” J. Math. Phys. 14, 104 (1973).ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    K. A. Bronnikov, “Scalar-tensor theory and scalar charge,” Acta Phys. Pol. B 4, 251 (1973).MathSciNetGoogle Scholar
  7. 7.
    K. A. Bronnikov, K. A. Baleevskikh, and M. V. Skvortsova, “Wormholes with fluid sources: A no-go theorem and new examples,” Phys. Rev. D 96, 124039 (2017); arXiv: 1708. 02324.ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    V. Bozza, “Gravitational lensing in the strong field limit,” Phys. Rev. D 66, 103001 (2002).ADSCrossRefGoogle Scholar
  9. 9.
    Naoki Tsukamoto, “Strong deflection limit analysis and gravitational lensing of an Ellis wormhole,” Phys. Rev. D 94, 124001 (2016); arXiv: 1607. 07022ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    Volker Perlick, “On the exact gravitational lens equation in spherically symmetric and static spacetimes,” Phys. Rev. D 69, 064017 (2004); gr-qc/0307072.ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    Kimet Jusufi and Ali Övgün, “Gravitational lensing by rotating wormholes,” Phys. Rev. D 97, 024042 (2018); arXiv: 1708. 06725ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    Rajibul Shaikh, Pritam Banerjee, Suvankar Paul, and Tapobrata Sarkar, “A novel gravitational lensing feature by wormholes,” arXiv: 1811. 08245.Google Scholar
  13. 13.
    I. Z. Fisher, “Scalar mesostatic field with regard for gravitational effects,” Zh. Eksp. Teor. Fiz. 18, 636 (1948); gr-qc/9911008.Google Scholar
  14. 14.
    K. A. Bronnikov and S. G. Rubin, Black Holes, Cosmology, and Extra Dimensions (World Scientific, Singapore, 2012).CrossRefzbMATHGoogle Scholar
  15. 15.
    Homer G. Ellis. “Cosmology without Einstein’s assumption that inertial mass produces gravity,” Int. J. Mod. Phys. D 24, 1550069 (2015); gr-qc/0701012.ADSMathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    J. A. Gonzalez, F. S. Guzman, and O. Sarbach, “Instability of wormholes supported by a ghost scalar field,” I. Linear stability analysis. Class. Quantum Grav. 26, 015010 (2009).ADSCrossRefzbMATHGoogle Scholar
  17. 17.
    K. A. Bronnikov, J. C. Fabris, and A. Zhidenko, “On the stability of scalar-vacuum space-times,” Euro Phys. J. C 71, 1791 (2011); arXiv: 1109. 6576.ADSCrossRefGoogle Scholar
  18. 18.
    K. A. Bronnikov, R. Konoplya, and A. Zhidenko, “Instabilities of wormholes and regular black holes supported by a phantom scalar field,” Phys. Rev. D 86, 024028 (2012); arxiv: 1205. 2224.ADSCrossRefGoogle Scholar
  19. 19.
    K. A. Bronnikov, L. N. Lipatova, I. D. Novikov, and A. A. Shatskiy, “Example of a stable wormhole in general relativity,” Grav. Cosmol. 19, 269 (2013); arXiv: 1312. 6929ADSMathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    K. A. Bronnikov and S.-W. Kim, “Possiblewormholes in a brane world,” Phys. Rev. D 67, 064027 (2003).ADSMathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    T. Shiromizu, K. Maeda, and M. Sasaki, “The Einstein equations on the 3-brane world,” Phys. Rev. D 62, 024012 (2000).ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    K. A. Bronnikov and P. A. Korolyov, “On wormholes with long throats and the stability problem,” Grav. Cosmol. 23, 273 (2017); arXiv: 1705. 05906.ADSMathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    K. A. Bronnikov, M. V. Skvortsova, and A. A. Starobinsky, “Notes on wormhole existence in scalartensor and f(R) gravity,” Grav. Cosmol. 16, 216 (2010); arXiv: 1005. 3262.ADSCrossRefzbMATHGoogle Scholar
  24. 24.
    K. A. Bronnikov, “Scalar fields as sources for wormholes and regular black holes,” Particles 1, 5 (2018); arXiv: 1802. 00098.CrossRefGoogle Scholar
  25. 25.
    K. A. Bronnikov and S. V. Sushkov, “Trapped ghosts: A new class of wormholes,” Class. Quantum Grav. 27, 095022 (2010); arXiv: 1001. 3511.ADSMathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Center for Gravitation and Fundamental MetrologyVNIIMSMoscowRussia
  2. 2.Peoples’ Friendship University of Russia (RUDN University)MoscowRussia
  3. 3.National Research Nuclear University “MEPhI” (Moscow Engineering Physics Institute)MoscowRussia

Personalised recommendations