- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Strong gravitational lensing by Kerr and Kerr-Newman black holes

Tien Hsieh, Da-Shin Lee*, and Chi-Yong Lin†

  • Department of Physics, National Dong Hwa University, Hualien 97401, Taiwan, Republic of China

  • *dslee@gms.ndhu.edu.tw
  • †lcyong@gms.ndhu.edu.tw
PDF

Phys. Rev. D 103, 104063 – Published 28 May, 2021

DOI: https://doi.org/10.1103/PhysRevD.103.104063

Abstract

We study the strong gravitational lensing due to the Kerr black holes with angular momentum a and the Kerr-Newman black holes with additional charge Q. We first derive the analytical expressions of the deflection angles of light rays that particularly diverge as they travel near the photon sphere. In this strong deflection limit, the light rays can circle around the black hole multiple times before reaching the observer, giving relativistic images. The obtained analytical expressions are then applied to compute the angular positions of relativistic images due to the supermassive galactic black holes. In this work, we focus on the outermost image with reference to the optical axis. We find that its angular separation from the one closest to the optical axis increases with the increase of angular momentum a of the black holes for light rays in direct orbits. Additionally, the effects of the charge Q of black holes also increase the angular separation of the outermost image from the others for both direct and retrograde orbits. The potentially increasing observability of the relativistic images from the effects of angular momentum and charge of the black holes will be discussed.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (33)

  1. C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (W. H. Freeman and Company, San Francisco, 1973).
  2. J. B. Hartle, Gravity: An Introduction to Einstein’s General Relativity (Addison-Wesley, Reading, MA, 2003).
  3. P. Schneider, J. Ehlers, and E. E. Falco, Gravitational Lenses (Springer-Verlag, New York, Berlin, Heidelberg, 1992).
  4. K. S. Virbhadra and G. F. R. Ellis, Schwarzschild black hole lensing, Phys. Rev. D 62, 084003 (2000).
  5. S. Frittelli, T. P. Kling, and E. T. Newman, Spacetime perspective of Schwarzschild lensing, Phys. Rev. D 61, 064021 (2000).
  6. V. Bozza, S. Capozziello, G. Iovane, and G. Scarptta, Strong field limit of black hole gravitational lensing, Gen. Relativ. Gravit. 33, 1535 (2001).
  7. V. Bozza, Gravitational lensing in the strong field limit, Phys. Rev. D 66, 103001 (2002).
  8. V. Bozza, Quasiequatorial gravitational lensing by spinning black holes in the strong field limit, Phys. Rev. D 67, 103006 (2003).
  9. V. Bozza, Gravitational lensing by black holes, Gen. Relativ. Gravit. 42, 2269 (2010).
  10. E. F. Eiroa, G. E. Romero, and D. F. Torres, Reissner-Nordstrom black hole lensing, Phys. Rev. D 66, 024010 (2002).
  11. S. V. Iyer and A. O. Petters, Light’s bending angle due to black holes: From the photon sphere to infinity, Gen. Relativ. Gravit. 39, 1563 (2007).
  12. N. Tsukamoto, Deflection angle in the strong deflection limit in a general asymptotically flat, static, spherically symmetric space-time, Phys. Rev. D 95, 064035 (2017).
  13. N. Tsukamoto and Y. Gong, Retrolensing by a charged black hole, Phys. Rev. D 95, 064034 (2017).
  14. K. S. Virbhadra and C. R. Keeton, Time delay and magnification centroid due to gravitational lensing by black holes and naked singularities, Phys. Rev. D 77, 124014 (2008).
  15. R. Shaikh, P. Banerjee, S. Paul, and T. Sarkar, Strong gravitational lensing by wormholes, J. Cosmol. Astropart. Phys. 07 (2019) 028.
  16. D. Richstone et al., Supermassive black holes and the evolution of galaxies, Nature (London) 14, 395 (1998).
  17. A. Ghez, B. L. Klein, M. Morris, and E. E. Becklin, High proper-motion stars in the vicinity of Sagittarius A*: Evidence for a supermassive black hole at the center of our galaxy, Astrophys. J. 509, 678 (1998).
  18. R. Schodel et al., A star in a 15.2-year orbit around the black hole at the centre of the Milky Way, Nature (London) 419, 694 (2002).
  19. K. Akiyama et al. (Event Horizon Telescope Collaboration), First M87 event horizon telescope results. I. The shadow of the supermassive black hole, Astrophys. J. 875, L1 (2019).
  20. K. Akiyama et al. (Event Horizon Telescope Collaboration), First M87 event horizon telescope results. V. Physical origin of the asymmetric ring, Astrophys. J. 875, L5 (2019).
  21. K. Akiyama et al., Event horizon telescope collaboration, First M87 event horizon telescope results. VI. The shadow and mass of the central black hole, Astrophys. J. 875, L6 (2019).
  22. S. V. Iyer and E. C. Hansen, Light’s bending angle in the equatorial plane of a Kerr black hole, Phys. Rev. D 80, 124023 (2009).
  23. Y.-W. Hsiao, D.-S. Lee, and C.-Y. Lin, Equatorial light bending around Kerr-Newman black holes, Phys. Rev. D 101, 064070 (2020).
  24. J. R. Wilson, Some magnetic effects in stellar collapse and accretion, Ann. N.Y. Acad. Sci. 262, 123 (1975).
  25. T. Damour, R. Hanni, R. Ruffini, and J. Wilson, Regions of magnetic support of a plasma around a black hole, Phys. Rev. D 17, 1518 (1978).
  26. C.-Y. Liu, D.-S. Lee, and C.-Y. Lin, Geodesic motion of neutral particles around a Kerr-Newman black hole, Classical Quantum Gravity 34, 235008 (2017).
  27. C. Jiang and W. Lin, Post-Newtonian light propagation in Kerr-Newman spacetime, Phys. Rev. D 97, 024045 (2018).
  28. G. V. Kraniotis, Gravitational lensing and frame dragging of light in the Kerr-Newman and the Kerr-Newman (anti) de Sitter black hole spacetimes, Gen. Relativ. Gravit. 46, 1818 (2014).
  29. J. S. Ulvestad, Goals of the ARISE Space VLBI Mission, New Astron. Rev. 43, 531 (1999).
  30. M. D. Johnson et al., Universal interferometric signatures of a black hole’s photon ring, Sci. Adv. 6, eaaz1310 (2020).
  31. G. N. Gyulchev and S. S. Yazadjiev, Kerr-Sen dilaton-axion black hole lensing in the strong deflection limit, Phys. Rev. D 75, 023006 (2007).
  32. S. E. Gralla and A. Lupsasca, Null geodesics of the Kerr exterior, Phys. Rev. D 101, 044032 (2020).
  33. S. E. Gralla and A. Lupsasca, Lensing by Kerr black holes, Phys. Rev. D 101, 044031 (2020).

Outline

Information

Phys. Rev. D 103, 104063– Published 28 May, 2021
  • Received 28 January 2021
  • Accepted 30 April 2021
Crossmark - Check for updates button

© 2021 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation