Relativistic rings due to Schwarzschild gravitational lensing

O.Yu. Tsupko1 and G.S. Bisnovatyi-Kogan2


Strong gravitational lensing in the Schwarzschild metric is considered in the case when the source, a point lens, and the observer are situated on a straight line. Angular sizes and magnification factors are calculated for relativistic rings formed by the photons which undergo one or several turns around the black hole.


  1. W. Ames and K. Thorne, ApJ 151, 659, (1968).
  2. G. S. Bisnovatyi-Kogan and A. A. Ruzmaikin, Astrophys. Space Sci., 28, 45 (1974).
  3. G. S. Bisnovatyi-Kogan and O. Yu. Tsupko, Astrophysics 51, 99 (2008).
  4. P. V. Bliokh and A. A. Minakov, Gravitational Lenses (Naukova Dumka, Kiev, 1989) (in Russian).
  5. V. Bozza and M. Sereno, Phys. Rev. D 73, 103004 (2006).
  6. V. Bozza, S. Capozziello, G. Iovane, and G. Scarpetta, Gen. Rel. Grav. 33 1535 (2001).
  7. V. Bozza, Phys. Rev. D 66, 103001 (2002).
  8. C. Darwin, Proc Roy. Soc. London, Series A, Mathematical and Physical Sciences, 249 (1257), 180 (1959).
  9. S. Frittelli, T. P. Kling, and E. T. Newman, Phys. Rev. D 61, 064021 (2000).
  10. C. R. Keeton and A. O. Petters, Phys. Rev. D 72, 104006 (2005).
  11. L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Pergamon, Oxford, 1993).
  12. C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, New York, 1973).
  13. P. Schneider, J. Ehlers, and E. Falco, Gravitational Lensing (Springer-Verlag, Berlin, 1992).
  14. K. S. Virbhadra and G. F. R. Ellis, Phys. Rev. D 62, 084003, 2000.
For more information about this paper please visit Springer's Home Page of this paper.

Back to The Contents Page