Skip to main content
SpringerLink
Log in

Gravitational lensing by a rotating massive object in a plasma

  • Original Article
  • Published:
Astrophysics and Space Science Aims and scope Submit manuscript

Abstract

We study gravitational lensing in the vicinity of a slowly rotating massive object surrounded by a plasma. We have studied two effects: (i) the influence of the frame dragging on the deflection angle of the light ray in the presence of plasma (ii) Faraday rotation of the polarization plane of the light. We derive the expression for the lensing angle in a non-diagonal space-time in the weak field regime in the presence of plasma and discuss it for the spacetime metric of the slowly rotating object. The obtained deflection angle depends on (i) the frequency of the electromagnetic wave, due to the dispersion properties of the plasma; (ii) the gravitational mass M; and (iii) the angular momentum J of the gravitational lens. We studied the influence of rotation of the gravitational lens on the magnification of brightness of the source star in the case of microlensing and have shown that it is negligibly small. For the completeness of our study the effect of the Faraday rotation of the polarization plane is considered.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  • Alcock, C., Akerlof, C.W., Allsman, R.A., Axelrod, T.S., Bennett, D.P., Chan, S., Cook, K.H., Freeman, K.C., Griest, K., Marshall, S.L., Park, H.-S., Perlmutter, S., Peterson, B.A., Pratt, M.R., Quinn, P.J., Rodgers, A.W., Stubbs, C.W., Sutherland, W.: Nature 365, 621 (1993)

    Article  ADS  Google Scholar 

  • Arifov, Ya.L.: General Theory of Relativity and Gravitation, 2nd edn. Fan, Tashkent (1983). 303 pp., in Russian

    Google Scholar 

  • Aubourg, E., Bareyre, P., Brehin, S., Gros, M., Lachieze-Rey, M., Laurent, B., Lesquoy, E., Magneville, C., Milsztajn, A., Moscosco, L., Queinnec, F., Rich, J., Spiro, M., Vigroux, L., Zylberajch, S., Ansari, R., Cavalier, F., Moniez, M., Beaulieu, J.-P., Ferlet, R., Grison, Ph., Vidal-Madjar, A., Guibert, J., Moreau, O., Tajahmady, F., Maurice, E., Prevot, L., Gry, C.: Nature 365, 623 (1993)

    Article  ADS  Google Scholar 

  • Beskin, V.S.: Astron. Zh. Pisma 16, 665 (1990). English transl. Soviet Astron. Lett. 16, 286

    ADS  Google Scholar 

  • Beskin, V.S.: MHD Flows in Compact Astrophysical Objects: Accretion, Winds and Jets. Extraterrestrial Physics & Space Sciences. Springer, Berlin (2009)

    Google Scholar 

  • Bisnovatyi-Kogan, G.S., Tsupko, Yu.O.: Gravit. Cosmol. 15, 20 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Bisnovatyi-Kogan, G.S., Tsupko, O.Yu.: Mon. Not. R. Astron. Soc. 404, 1790 (2010)

    ADS  Google Scholar 

  • Bozza, V.: Gen. Relativ. Gravit. 42, 2269 (2010)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Brandenburg, A., Subramanian, K.: Phys. Rep. 417, 1 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  • Brodutch, A., Demarie, T.F., Terno, D.R.: Phys. Rev. D 84, 104043 (2011)

    Article  ADS  Google Scholar 

  • Ciufolini, I., Wheeler, J.A.: Gravitation and Inertia. Princeton University Press, Princeton (1995)

    MATH  Google Scholar 

  • De Paolis, F., Ingrosso, G., Nucita, A.A., Qadir, A., Zakharov, A.F.: Gen. Relativ. Gravit. 43, 977 (2011)

    Article  ADS  MATH  Google Scholar 

  • Faraday, M.: Philos. Trans. R. Soc. Lond. 136, 1 (1846)

    Article  Google Scholar 

  • Geppert, U.: Becker, W. (ed.): Neutron Stars and Pulsars. Astrophys. Space Sci. Library, vol. 357, p. 319. Springer, Berlin (2009)

    Chapter  Google Scholar 

  • Gnedin, Yu.N., Buliga, S.D., Silant’ev, N.A., Natsvlishvili, T., Piotrovich, M.Yu.: Astrophys. Space Sci. 342, 137 (2012)

    Article  ADS  Google Scholar 

  • Hartle, J.B.: Gravity: An Introduction to Einstein’s General Relativity. Pearson Education (2003)

  • Hartle, J.B., Thorne, K.S.: Astrophys. J. 153, 807 (1968)

    Article  ADS  Google Scholar 

  • Ishihara, H., Takahashi, M., Tomimatsu, A.: Phys. Rev. D 38, 2 (1988)

    Article  MathSciNet  Google Scholar 

  • Landau, L.D., Lifshitz, E.M.: The Classical Theory of Fields. Pergamon, Elmsford (1971)

    Google Scholar 

  • Mofiz, U.A., Ahmedov, B.J.: Astrophys. J. 542, 484 (2000)

    Article  ADS  Google Scholar 

  • Morales, J.A., Saez, D.: Phys. Rev. D 75, 043011 (2007)

    Article  ADS  Google Scholar 

  • Morozova, V.S., Ahmedov, B.J., Kagramanova, V.G.: Astrophys. J. 684, 1359 (2008)

    Article  ADS  Google Scholar 

  • Muslimov, A., Harding, A.K.: Astrophys. J. 485, 735 (1997)

    Article  ADS  Google Scholar 

  • Muslimov, A.G., Tsygan, A.I.: Mon. Not. R. Astron. Soc. 255, 61 (1992)

    MathSciNet  ADS  Google Scholar 

  • Narasimha, D., Chitre, S.M.: Curr. Sci. 93, 1506 (2008)

    Google Scholar 

  • Paczyński, B.: Astrophys. J. 304, 1 (1986)

    Article  ADS  Google Scholar 

  • Paczyński, B.: Annu. Rev. Astron. Astrophys. 34, 419 (1996)

    Article  ADS  Google Scholar 

  • Patnaik, A.R., Menten, K.M., Porcas, R.W., Kemball, A.J.: Grav. Lens. 237 (2001)

  • Rezzolla, L., Ahmedov, B.J., Miller, J.C.: Mon. Not. R. Astron. Soc. 322, 723 (2001a). Erratum 338, 816 (2003)

    Article  ADS  Google Scholar 

  • Rezzolla, L., Ahmedov, B.J., Miller, J.C.: Found. Phys. 31, 1051 (2001b)

    Article  Google Scholar 

  • Saikia, D.J., Salter, C.J.: Annu. Rev. Astron. Astrophys. 26, 93 (1988)

    Article  ADS  Google Scholar 

  • Schee, J., Stuchlik, Z.: Int. J. Mod. Phys. D 18, 983 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Sereno, M.: Phys. Rev. D 69, 087501 (2004)

    Article  ADS  Google Scholar 

  • Shafee, R., Narayan, R., McClintock, J.E.: Astrophys. J. 676, 549 (2008)

    Article  ADS  Google Scholar 

  • Silant’ev, N.A.: Astron. Astrophys. 383, 326 (2002)

    Article  ADS  Google Scholar 

  • Silant’ev, N.A.: Astron. Astrophys. 433, 1117 (2005)

    Article  ADS  Google Scholar 

  • Silant’ev, N.A., Piotrovich, M.Yu., Gnedin, Yu.N., Natsvlishvili, T.M.: Astron. Astrophys. 507, 171 (2009)

    Article  ADS  Google Scholar 

  • Silant’ev, N.A., Gnedin, Yu.N., Buliga, S.D., Piotrovich, M.Yu., Natsvlishvili, T.M.: Astrophys. Bull. 68, 14 (2013a)

    Article  ADS  Google Scholar 

  • Silant’ev, N.A., Gnedin, Yu.N., Piotrovich, M.Yu., Natsvlishvili, T.M.: Astrophys. Bull. 68, 14 (2013b)

    Article  ADS  Google Scholar 

  • Skrotskii, G.V.: Sov. Phys. Dokl. 2, 226 (1957)

    ADS  MATH  Google Scholar 

  • Steiner, J.F., McClintock, J.E., Remillard, R.A., Narayan, R., Gou, L.: Astrophys. J. Lett. 701, L83 (2009)

    Article  ADS  Google Scholar 

  • Synge, J.L.: Relativity: the General Theory. North-Holland, Amsterdam (1960)

    MATH  Google Scholar 

  • Thorman, P. Jr.: Faraday Rotation in the Interstellar Medium (2001)

  • Tsupko, O.Yu. Bisnovatyi-Kogan, G.S.: Gravit. Cosmol. 18, 117 (2012)

    Article  ADS  MATH  Google Scholar 

  • Udalski, A., Szymanski, M., Kaluzny, J., Kubiak, M., Krzeminski, W., Mateo, M., Preston, G.W., Paczynski, B.: Acta Astron. 43, 289 (1993)

    ADS  Google Scholar 

  • Wambganss, J.: In: Meylan, G., Jetzer, P., North, P. (eds.) Gravitational Lensing: Strong, Weak and Micro, p. 453 (2006)

    Chapter  Google Scholar 

  • Zakharov, A.F., De Paolis, F., Ingrosso, G., Nucita, A.A.: Astron. Astrophys. 442, 795 (2005b)

    Article  ADS  Google Scholar 

  • Zakharov, A.F., Nucita, A.A., DePaolis, F., Ingrosso, G.: New Astron. 10, 479 (2005a)

    Article  ADS  Google Scholar 

  • Zanotti, O., Morozova, V.S., Ahmedov, B.J.: Astron. Astrophys. 540, A126 (2012)

    Article  ADS  Google Scholar 

  • Zavala, R.T., Taylor, G.B.: New Astron. Rev. 47, 589 (2003)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This research is supported in part by the projects F2-FA-F113, FE2-FA-F134 of the UzAS and by the ICTP through the OEA-PRJ-29 projects. BA acknowledges the German Academic Exchange Service (DAAD) and the ENSF, Trieste, Italy travel grants. BA and AT greatly acknowledge the hospitality at the Max-Planck-Institut für Gravitationsphysik, Potsdam.

Author information

Authors and Affiliations

  1. Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, 14476, Golm, Germany

    V. S. Morozova

  2. Institute of Nuclear Physics, Ulughbek, Tashkent, 100214, Uzbekistan

    V. S. Morozova, B. J. Ahmedov & A. A. Tursunov

  3. Ulugh Begh Astronomical Institute, Astronomicheskaya 33, Tashkent, 100052, Uzbekistan

    B. J. Ahmedov & A. A. Tursunov

  4. The Abdus Salam International Centre for Theoretical Physics, 34151, Trieste, Italy

    B. J. Ahmedov

Authors
  1. V. S. Morozova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. J. Ahmedov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. A. Tursunov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. S. Morozova.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Morozova, V.S., Ahmedov, B.J. & Tursunov, A.A. Gravitational lensing by a rotating massive object in a plasma. Astrophys Space Sci 346, 513–520 (2013). https://doi.org/10.1007/s10509-013-1458-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10509-013-1458-6

Keywords

Search

Navigation