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Analytical perturbations of relativistic images in Kerr space-time

Published 15 Mar 2024 in gr-qc and astro-ph.CO | (2403.10169v2)

Abstract: Light rays passing very close to black holes may wind several times before escaping. For any given electromagnetic source around the black hole, a distant observer would thus observe two infinite sequences of images on either side of the black hole. These images are generated by light rays performing an increasing numbers of loops. The strong deflection limit provides a simple analytic formalism to describe such higher order images for spherically symmetric metrics, while for axially symmetric black holes one typically resorts to numerical approaches. Here we present the leading order perturbation to higher order images when the black hole spin is turned on. We show that the images slide around the black hole shadow as an effect of space-time dragging. We derive analytical formulae for their shifts and the perturbation of their time delays. We also discuss how such simple analytical formulae for images by Kerr black holes can be of great help in many applications.

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References (69)
  1. C. Darwin, “The Gravity Field of a Particle,” Proceedings of the Royal Society of London Series A, vol. 249, no. 1257, pp. 180–194, Jan. 1959.
  2. H. C. Ohanian, “The black hole as a gravitational “lens”,” American Journal of Physics, vol. 55, no. 5, pp. 428–432, May 1987.
  3. R. d. Atkinson, “On light tracks near a very massive star,” Astronomical Journal, vol. 70, p. 517, Oct. 1965.
  4. H. Falcke, F. Melia, and E. Agol, “Viewing the shadow of the black hole at the galactic center,” The Astrophysical Journal Letters, vol. 528, no. 1, p. L13, 1999.
  5. ——, “The shadow of the black hole at the galactic center,” in AIP Conference Proceedings, vol. 522, no. 1.   American Institute of Physics, 2000, pp. 317–320.
  6. V. Perlick and O. Y. Tsupko, “Calculating black hole shadows: Review of analytical studies,” Physics Reports, vol. 947, pp. 1–39, 2022.
  7. Virbhadra and Ellis, “Schwarzschild black hole lensing,” Physical Review D, vol. 62, no. 8, p. 084003, 2000.
  8. V. Bozza, S. Capozziello, G. Iovane, and G. Scarpetta, “Strong Field Limit of Black Hole Gravitational Lensing,” General Relativity and Gravitation, vol. 33, no. 9, pp. 1535–1548, Sep. 2001.
  9. E. F. Eiroa, G. E. Romero, and D. F. Torres, “Reissner-nordström black hole lensing,” Physical Review D, vol. 66, no. 2, p. 024010, 2002.
  10. V. Bozza, “Gravitational lensing in the strong field limit,” Physical Review D, vol. 66, no. 10, p. 103001, Nov. 2002.
  11. V. Bozza and L. Mancini, “Time Delay in Black Hole Gravitational Lensing as a Distance Estimator,” General Relativity and Gravitation, vol. 36, no. 2, pp. 435–450, Feb. 2004.
  12. E. F. Eiroa and D. F. Torres, “Strong field limit analysis of gravitational retrolensing,” Physical Review D, vol. 69, no. 6, p. 063004, 2004.
  13. V. Bozza, F. De Luca, G. Scarpetta, and M. Sereno, “Analytic kerr black hole lensing for equatorial observers in the strong deflection limit,” Physical Review D, vol. 72, no. 8, p. 083003, 2005.
  14. V. Bozza, F. De Luca, and G. Scarpetta, “Kerr black hole lensing for generic observers in the strong deflection limit,” Physical Review D, vol. 74, no. 6, p. 063001, 2006.
  15. V. Bozza and G. Scarpetta, “Strong deflection limit of black hole gravitational lensing with arbitrary source distances,” Physical Review D, vol. 76, no. 8, p. 083008, 2007.
  16. V. Bozza, “Gravitational lensing by black holes,” General Relativity and Gravitation, vol. 42, no. 9, pp. 2269–2300, Sep. 2010.
  17. E. H. T. Collaboration et al., “First m87 event horizon telescope results. i. the shadow of the supermassive black hole,” arXiv preprint arXiv:1906.11238, 2019.
  18. K. Akiyama, A. Alberdi, W. Alef, J. C. Algaba, R. Anantua, K. Asada, R. Azulay, U. Bach, A.-K. Baczko, D. Ball et al., “First sagittarius a* event horizon telescope results. i. the shadow of the supermassive black hole in the center of the milky way,” The Astrophysical Journal Letters, vol. 930, no. 2, p. L12, 2022.
  19. S. E. Gralla, D. E. Holz, and R. M. Wald, “Black hole shadows, photon rings, and lensing rings,” Physical Review D, vol. 100, no. 2, p. 024018, 2019.
  20. S. E. Gralla and A. Lupsasca, “Lensing by kerr black holes,” Physical Review D, vol. 101, no. 4, p. 044031, 2020.
  21. ——, “Observable shape of black hole photon rings,” Physical Review D, vol. 102, no. 12, p. 124003, 2020.
  22. Q. Gan, P. Wang, H. Wu, and H. Yang, “Photon ring and observational appearance of a hairy black hole,” Physical Review D, vol. 104, no. 4, p. 044049, Aug. 2021.
  23. M. Wielgus, “Photon rings of spherically symmetric black holes and robust tests of non-Kerr metrics,” Physical Review D, vol. 104, no. 12, p. 124058, Dec. 2021.
  24. S. Hadar, M. D. Johnson, A. Lupsasca, and G. N. Wong, “Photon ring autocorrelations,” Physical Review D, vol. 103, no. 10, p. 104038, May 2021.
  25. D. Ayzenberg, “Testing gravity with black hole shadow subrings,” Classical and Quantum Gravity, vol. 39, no. 10, p. 105009, 2022.
  26. A. E. Broderick, D. W. Pesce, R. Gold, P. Tiede, H.-Y. Pu, R. Anantua, S. Britzen, C. Ceccobello, K. Chatterjee, Y. Chen et al., “The Photon Ring in M87*,” The Astrophysical Journal, vol. 935, no. 1, p. 61, 2022.
  27. E. Papoutsis, M. Bauböck, D. Chang, and C. F. Gammie, “Jets and rings in images of spinning black holes,” The Astrophysical Journal, vol. 944, no. 1, p. 55, 2023.
  28. A. E. Broderick, K. Salehi, and B. Georgiev, “Shadow implications: What does measuring the photon ring imply for gravity?” The Astrophysical Journal, vol. 958, no. 2, p. 114, 2023.
  29. D. W. Pesce, K. Haworth, G. J. Melnick, L. Blackburn, M. Wielgus, M. D. Johnson, A. Raymond, J. Weintroub, D. C. Palumbo, S. S. Doeleman et al., “Extremely long baseline interferometry with origins space telescope,” Astro2020: Decadal Survey on Astronomy and Astrophysics, APC white papers, no. 176, 2019.
  30. D. W. Pesce, D. C. M. Palumbo, R. Narayan, L. Blackburn, S. S. Doeleman, M. D. Johnson, C.-P. Ma, N. M. Nagar, P. Natarajan, and A. Ricarte, “Toward determining the number of observable supermassive black hole shadows,” The Astrophysical Journal, vol. 923, no. 2, p. 260, 2021.
  31. A. Andrianov, A. Baryshev, H. Falcke, I. Girin, T. de Graauw, V. Kostenko, V. Kudriashov, V. Ladygin, S. Likhachev, F. Roelofs et al., “Simulations of m87 and sgr a* imaging with the millimetron space observatory on near-earth orbits,” Monthly Notices of the Royal Astronomical Society, vol. 500, no. 4, pp. 4866–4877, 2021.
  32. A. Andrianov, S. Chernov, I. Girin, S. Likhachev, A. Lyakhovets, and Y. Shchekinov, “Flares and their echoes can help distinguish photon rings from black holes with space-Earth very long baseline interferometry,” Physical Review D, vol. 105, no. 6, p. 063015, Mar. 2022.
  33. M. D. Johnson, A. Lupsasca, A. Strominger, G. N. Wong, S. Hadar, D. Kapec, R. Narayan, A. Chael, C. F. Gammie, P. Galison, D. C. M. Palumbo, S. S. Doeleman, L. Blackburn, M. Wielgus, D. W. Pesce, J. R. Farah, and J. M. Moran, “Universal interferometric signatures of a black hole’s photon ring,” Science Advances, vol. 6, no. 12, p. eaaz1310, Mar. 2020.
  34. S. E. Gralla, A. Lupsasca, and D. P. Marrone, “The shape of the black hole photon ring: A precise test of strong-field general relativity,” Physical Review D, vol. 102, no. 12, p. 124004, 2020.
  35. E. Himwich, M. D. Johnson, A. Lupsasca, and A. Strominger, “Universal polarimetric signatures of the black hole photon ring,” Physical Review D, vol. 101, no. 8, p. 084020, Apr. 2020.
  36. A. E. Broderick, P. Tiede, D. W. Pesce, and R. Gold, “Measuring Spin from Relative Photon-ring Sizes,” The Astrophysical Journal, vol. 927, no. 1, p. 6, Mar. 2022.
  37. A. Eichhorn, A. Held, and P.-V. Johannsen, “Universal signatures of singularity-resolving physics in photon rings of black holes and horizonless objects,” Journal of Cosmology and Astroparticle Physics, vol. 2023, no. 01, p. 043, 2023.
  38. S. Staelens, D. R. Mayerson, F. Bacchini, B. Ripperda, and L. Küchler, “Black hole photon rings beyond general relativity,” Physical Review D, vol. 107, no. 12, p. 124026, 2023.
  39. P. Kocherlakota, L. Rezzolla, R. Roy, and M. Wielgus, “Extreme light bending in spherically-symmetric black hole spacetimes: Universal characteristics and strong-field tests of gravity,” arXiv preprint arXiv:2307.16841, 2023.
  40. L. F. D. da Silva, F. S. Lobo, G. J. Olmo, and D. Rubiera-Garcia, “Photon rings as tests for alternative spherically symmetric geometries with thin accretion disks,” Physical Review D, vol. 108, no. 8, p. 084055, 2023.
  41. J. P. Luminet, “Image of a spherical black hole with thin accretion disk.” Astronomy and Astrophysics, vol. 75, pp. 228–235, May 1979.
  42. A. Bhadra, “Gravitational lensing by a charged black hole of string theory,” Physical Review D, vol. 67, no. 10, p. 103009, May 2003.
  43. R. Whisker, “Strong gravitational lensing by braneworld black holes,” Physical Review D, vol. 71, no. 6, p. 064004, Mar. 2005.
  44. E. F. Eiroa, “Braneworld black hole gravitational lens: Strong field limit analysis,” Physical Review D, vol. 71, no. 8, p. 083010, Apr. 2005.
  45. ——, “Gravitational lensing by Einstein-Born-Infeld black holes,” Physical Review D, vol. 73, no. 4, p. 043002, Feb. 2006.
  46. A. Övgün, “Light deflection by Damour-Solodukhin wormholes and Gauss-Bonnet theorem,” Physical Review D, vol. 98, no. 4, p. 044033, Aug. 2018.
  47. N. Tsukamoto, “Strong deflection limit analysis and gravitational lensing of an Ellis wormhole,” Physical Review D, vol. 94, no. 12, p. 124001, Dec. 2016.
  48. ——, “Deflection angle in the strong deflection limit in a general asymptotically flat, static, spherically symmetric spacetime,” Physical Review D, vol. 95, no. 6, p. 064035, Mar. 2017.
  49. S. Chen and J. Jing, “Strong field gravitational lensing in the deformed Hořava-Lifshitz black hole,” Physical Review D, vol. 80, no. 2, p. 024036, Jul. 2009.
  50. A. Y. Bin-Nun, “Relativistic images in Randall-Sundrum II braneworld lensing,” Physical Review D, vol. 81, no. 12, p. 123011, Jun. 2010.
  51. N. Tsukamoto, “Gravitational lensing in the Simpson-Visser black-bounce spacetime in a strong deflection limit,” Physical Review D, vol. 103, no. 2, p. 024033, Jan. 2021.
  52. S. V. Iyer and A. O. Petters, “Light’s bending angle due to black holes: from the photon sphere to infinity,” General Relativity and Gravitation, vol. 39, no. 10, pp. 1563–1582, Oct. 2007.
  53. S. Chakraborty and S. SenGupta, “Strong gravitational lensing—a probe for extra dimensions and Kalb-Ramond field,” Journal of Cosmology and Astroparticle Physics, vol. 2017, no. 7, p. 045, Jul. 2017.
  54. G. Bisnovatyi-Kogan and O. Y. Tsupko, “Strong gravitational lensing by schwarzschild black holes,” Astrophysics, vol. 51, pp. 99–111, 2008.
  55. O. Y. Tsupko and G. S. Bisnovatyi-Kogan, “Gravitational lensing in plasma: Relativistic images at homogeneous plasma,” Physical Review D, vol. 87, no. 12, p. 124009, 2013.
  56. G. S. Bisnovatyi-Kogan and O. Y. Tsupko, “Analytical study of higher-order ring images of the accretion disk around a black hole,” Physical Review D, vol. 105, no. 6, p. 064040, 2022.
  57. O. Y. Tsupko, “Shape of higher-order images of equatorial emission rings around a Schwarzschild black hole: Analytical description with polar curves,” Physical Review D, vol. 106, no. 6, p. 064033, Sep. 2022.
  58. G. F. Aldi and V. Bozza, “Relativistic iron lines in accretion disks: the contribution of higher order images in the strong deflection limit,” Journal of Cosmology and Astroparticle Physics, vol. 2017, no. 2, p. 033, Feb. 2017.
  59. F. Aratore and V. Bozza, “Decoding a black hole metric from the interferometric pattern of the relativistic images of a compact source,” Journal of Cosmology and Astroparticle Physics, vol. 2021, no. 10, p. 054, 2021.
  60. S. E. Vázquez and E. P. Esteban, “Strong-field gravitational lensing by a Kerr black hole,” Nuovo Cimento B Serie, vol. 119, no. 5, p. 489, May 2004.
  61. S. Chen and J. Jing, “Strong gravitational lensing by a rotating non-Kerr compact object,” Physical Review D, vol. 85, no. 12, p. 124029, Jun. 2012.
  62. S.-W. Wei, Y.-X. Liu, C.-E. Fu, and K. Yang, “Strong field limit analysis of gravitational lensing in Kerr-Taub-NUT spacetime,” Journal of Cosmology and Astroparticle Physics, vol. 2012, no. 10, p. 053, Oct. 2012.
  63. S. U. Islam, J. Kumar, and S. G. Ghosh, “Strong gravitational lensing by rotating Simpson-Visser black holes,” Journal of Cosmology and Astroparticle Physics, vol. 2021, no. 10, p. 013, Oct. 2021.
  64. N. S. Barlow, S. J. Weinstein, and J. A. Faber, “An asymptotically consistent approximant for the equatorial bending angle of light due to Kerr black holes,” Classical and Quantum Gravity, vol. 34, no. 13, p. 135017, Jul. 2017.
  65. B. Carter, “Global structure of the kerr family of gravitational fields,” Physical Review, vol. 174, no. 5, p. 1559, 1968.
  66. K. Beckwith and C. Done, “Extreme gravitational lensing near rotating black holes,” Monthly Notices of the Royal Astronomical Society, vol. 359, no. 4, pp. 1217–1228, 2005.
  67. A. Chael, M. D. Johnson, and A. Lupsasca, “Observing the Inner Shadow of a Black Hole: A Direct View of the Event Horizon,” The Astrophysical Journal, vol. 918, no. 1, p. 6, Sep. 2021.
  68. G. V. Kraniotis, “Precise analytic treatment of Kerr and Kerr-(anti) de Sitter black holes as gravitational lenses,” Classical and Quantum Gravity, vol. 28, no. 8, p. 085021, Apr. 2011.
  69. V. Bozza, “Optical caustics of Kerr spacetime: The full structure,” Physical Review D, vol. 78, no. 6, p. 063014, Sep. 2008.
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Authors (2)

  1. Fabio Aratore 
  2. Valerio Bozza 

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