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Black hole images: A review

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Abstract

In recent years, unprecedented progress has been achieved regarding black holes’ observation through the electromagnetic channel. The images of the supermassive black holes M87* and Sgr A* released by the Event Horizon Telescope (EHT) Collaboration provided direct visual evidence for their existence, which has stimulated further studies on various aspects of the compact celestial objects. Moreover, the information stored in these images provides a new way to understand the pertinent physical processes that occurred near the black holes, to test alternative theories of gravity, and to furnish insight into fundamental physics. In this review, we briefly summarize the recent developments on the topic. In particular, we elaborate on the features and formation mechanism of black hole shadows, the properties of black hole images illuminated by the surrounding thin accretion disk, and the corresponding polarization patterns. The potential applications of the relevant studies are also addressed.

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References

  1. K. Akiyama, et al. (The Event Horizon Telescope Collaboration), Astrophys. J. 875, L1 (2019), ar**v: 1906.11238.

    Article  ADS  Google Scholar 

  2. K. Akiyama, et al. (The Event Horizon Telescope Collaboration), Astrophys. J. 875, L2 (2019), ar**v: 1906.11239.

    Article  ADS  Google Scholar 

  3. K. Akiyama, et al. (The Event Horizon Telescope Collaboration), Astrophys. J. 875, L3 (2019), ar**v: 1906.11240.

    Article  ADS  Google Scholar 

  4. K. Akiyama, et al. (The Event Horizon Telescope Collaboration), Astrophys. J. 875, L4 (2019), ar**v: 1906.11241.

    Article  ADS  Google Scholar 

  5. K. Akiyama, et al. (The Event Horizon Telescope Collaboration), Astrophys. J. 875, L5 (2019), ar**v: 1906.11242.

    Article  ADS  Google Scholar 

  6. K. Akiyama, et al. (The Event Horizon Telescope Collaboration), Astrophys. J. 875, L6 (2019), ar**v: 1906.11243.

    Article  ADS  Google Scholar 

  7. K. Akiyama, et al. (The Event Horizon Telescope Collaboration), Astrophys. J. Lett. 930, L17 (2022).

    Article  ADS  Google Scholar 

  8. H. Falcke, F. Melia, and E. Agol, Astrophys. J. 528, L13 (2000), ar**v: astro-ph/9912263.

    Article  ADS  Google Scholar 

  9. J. L. Synge, Mon. Not. R. Astron. Soc. 131, 463 (1966).

    Article  ADS  Google Scholar 

  10. J. M. Bardeen, in Les Houches Summer School of Theoretical Physics: Black Holes (Les Houches, 1973), p. 215.

  11. C. T. Cunningham, Astrophys. J. 202, 788 (1975).

    Article  ADS  Google Scholar 

  12. S. Chandrasekhar, Fundam. Theor. Phys. 9, 5 (1984).

    Google Scholar 

  13. K. Akiyama, et al. (The Event Horizon Telescope Collaboration), Astrophys. J. Lett. 910, L12 (2021), ar**v: 2105.01169.

    Article  ADS  Google Scholar 

  14. K. Akiyama, et al. (The Event Horizon Telescope Collaboration), Astrophys. J. Lett. 910, L13 (2021), ar**v: 2105.01173.

    Article  ADS  Google Scholar 

  15. P. V. P. Cunha, C. A. R. Herdeiro, and E. Radu, Phys. Rev. D 96, 024039 (2017), ar**v: 1705.05461.

    Article  ADS  Google Scholar 

  16. J. Grover, and A. Wittig, Phys. Rev. D 96, 024045 (2017), ar**v: 1705.07061.

    Article  ADS  MathSciNet  Google Scholar 

  17. V. Perlick, Living Rev. Relativ. 7, 9 (2004).

    Article  ADS  Google Scholar 

  18. R. D. Blandford, and R. Narayan, Annu. Rev. Astron. Astrophys. 30, 311 (1992).

    Article  ADS  Google Scholar 

  19. S. Refsdal, and J. Surdej, Rep. Prog. Phys. 57, 117 (1994).

    Article  ADS  Google Scholar 

  20. P. V. P. Cunha, and C. A. R. Herdeiro, Gen. Relativ. Gravit. 50, 42 (2018), ar**v: 1801.00860.

    Article  ADS  Google Scholar 

  21. V. Perlick, and O. Y. Tsupko, Phys. Rep. 947, 1 (2022), ar**v: 2105.07101.

    Article  ADS  MathSciNet  Google Scholar 

  22. M. Wang, S. Chen, and J. **g, Commun. Theor. Phys. 74, 097401 (2022), ar**v: 2205.05855.

    Article  ADS  Google Scholar 

  23. M. Wang, S. Chen, and J. **g, J. Cosmol. Astropart. Phys. 2017, 51 (2017), ar**v: 1707.09451.

    Article  Google Scholar 

  24. I. Sengo, P. V. P. Cunha, C. A. R. Herdeiro, and E. Radu, ar**v: 2209.06237.

  25. L. Amarilla, E. F. Eiroa, and G. Giribet, Phys. Rev. D 81, 124045 (2010), ar**v: 1005.0607.

    Article  ADS  MathSciNet  Google Scholar 

  26. S. Dastan, R. Saffari, and S. Soroushfar, Eur. Phys. J. Plus 137, 1002 (2022), ar**v: 1606.06994.

    Article  Google Scholar 

  27. F. Long, S. Chen, M. Wang, and J. **g, Eur. Phys. J. C 80, 1180 (2020), ar**v: 2009.07508.

    Article  ADS  Google Scholar 

  28. A. Stepanian, S. Khlghatyan, and V. G. Gurzadyan, Eur. Phys. J. Plus 136, 127 (2021), ar**v: 2101.08261.

    Article  Google Scholar 

  29. V. A. Prokopov, S. O. Alexeyev, and O. I. Zenin, J. Exp. Theor. Phys. 135, 91 (2022), ar**v: 2107.01115.

    Article  ADS  Google Scholar 

  30. Z. Younsi, D. Psaltis, and F. Özel, ar**v: 2111.01752.

  31. B. Carter, Phys. Rev. 174, 1559 (1968).

    Article  ADS  Google Scholar 

  32. P. V. P. Cunha, C. A. Herdeiro, E. Radu, and H. F. Rúnarsson, Phys. Rev. Lett. 115, 211102 (2015), ar**v: 1509.00021.

    Article  ADS  Google Scholar 

  33. F. H. Vincent, E. Gourgoulhon, C. Herdeiro, and E. Radu, Phys. Rev. D 94, 084045 (2016), ar**v: 1606.04246.

    Article  ADS  Google Scholar 

  34. P. V. P. Cunha, J. Grover, C. Herdeiro, E. Radu, H. Rúnarsson, and A. Wittig, Phys. Rev. D 94, 104023 (2016), ar**v: 1609.01340.

    Article  ADS  Google Scholar 

  35. M. Wang, S. Chen, and J. **g, Phys. Rev. D 97, 064029 (2018), ar**v: 1710.07172.

    Article  ADS  MathSciNet  Google Scholar 

  36. M. Wang, S. Chen, and J. **g, Phys. Rev. D 98, 104040 (2018), ar**v: 1801.02118.

    Article  ADS  MathSciNet  Google Scholar 

  37. M. Wang, S. Chen, J. Wang, and J. **g, Eur. Phys. J. C 80, 110 (2020), ar**v: 1904.12423.

    Article  ADS  Google Scholar 

  38. A. Bohn, W. Throwe, F. Hébert, K. Henriksson, D. Bunandar, M. A. Scheel, and N. W. Taylor, Class. Quantum Grav. 32, 065002 (2015), ar**v: 1410.7775.

    Article  ADS  Google Scholar 

  39. A. Riazuelo, Int. J. Mod. Phys. D 28, 1950042 (2018), ar**v: 1511.06025.

    Article  ADS  MathSciNet  Google Scholar 

  40. C. M. Claudel, K. S. Virbhadra, and G. F. R. Ellis, J. Math. Phys. 42, 818 (2001), ar**v: gr-qc/0005050.

    Article  ADS  MathSciNet  Google Scholar 

  41. K. S. Virbhadra, and G. F. R. Ellis, Phys. Rev. D 65, 103004 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  42. C.-K. Qiao, ar**v: 2208.01771.

  43. P. V. P. Cunha, E. Berti, and C. A. R. Herdeiro, Phys. Rev. Lett. 119, 251102 (2017), ar**v: 1708.04211.

    Article  ADS  MathSciNet  Google Scholar 

  44. P. V. P. Cunha, C. Herdeiro, E. Radu, and N. Sanchis-Gual, ar**v: 2207.13713.

  45. W. L. Qian, S. Chen, C. G. Shao, B. Wang, and R. H. Yue, Eur. Phys. J. C 82, 91 (2022), ar**v: 2102.03820.

    Article  ADS  Google Scholar 

  46. S. Li, A. A. Abdujabbarov, and W. B. Han, Eur. Phys. J. C 81, 649 (2021), ar**v: 2103.08104.

    Article  ADS  Google Scholar 

  47. C. Bambi, in 14th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics, and Relativistic Field Theories (World Scientific, Singapore, 2017), p. 3494.

    Google Scholar 

  48. M. Ghasemi-Nodehi, Z. Li, and C. Bambi, Eur. Phys. J. C 75, 315 (2015), ar**v: 1506.02627.

    Article  ADS  Google Scholar 

  49. R. Kumar, and S. G. Ghosh, Astrophys. J. 892, 78 (2020), ar**v: 1811.01260.

    Article  ADS  Google Scholar 

  50. L. Medeiros, D. Psaltis, and F. Özel, Astrophys. J. 896, 7 (2020), ar**v: 1907.12575.

    Article  ADS  Google Scholar 

  51. Z. Carson, and K. Yagi, Phys. Rev. D 101, 084030 (2020), ar**v: 2002.01028.

    Article  ADS  MathSciNet  Google Scholar 

  52. G. Mingotti, F. Topputo, and F. Bernelli-Zazzera, Celest. Mech. Dyn. Astr. 105, 61 (2009).

    Article  ADS  Google Scholar 

  53. W. S. Koon, M. W. Lo, J. E. Marsden, and S. D. Ross, Celest. Mech. Dyn. Astr. 81, 63 (2001).

    Article  ADS  Google Scholar 

  54. M. Henon, Generating Families in the Restricted Three-Body Problem (Springer, Heidelberg, 1997).

    MATH  Google Scholar 

  55. D. L. Richardson, Celest. Mech. 22, 241 (1980).

    Article  ADS  Google Scholar 

  56. J. P. Luminet, Am. Acad. Pediatr. 75, 228 (1979).

    Google Scholar 

  57. D. N. Page, and K. S. Thorne, Astrophys. J. 191, 499 (1974).

    Article  ADS  Google Scholar 

  58. G. S. Bisnovatyi-Kogan, and O. Y. Tsupko, Phys. Rev. D 105, 064040 (2022), ar**v: 2201.01716.

    Article  ADS  Google Scholar 

  59. T. Bronzwaer, and H. Falcke, Astrophys. J. 920, 155 (2021), ar**v: 2108.03966.

    Article  ADS  Google Scholar 

  60. T. Bronzwaer, J. Davelaar, Z. Younsi, M. Moscibrodzka, H. Olivares, Y. Mizuno, J. Vos, and H. Falcke, Mon. Not. R. Astron. Soc. 501, 4722 (2021), ar**v: 2011.00069.

    Article  ADS  Google Scholar 

  61. O. James, E. Tunzelmann, P. Franklin, and K. S. Thorne, Class. Quantum Grav. 32, 065001 (2015), ar**v: 1502.03808.

    Article  ADS  Google Scholar 

  62. S. U. Viergutz, Am. Acad. Pediatr. 272, 355 (1993).

    MathSciNet  Google Scholar 

  63. S. U. Viergutz, Astrophys. Space Sci. 205, 155 (1993).

    Article  ADS  Google Scholar 

  64. J. P. S. Lemos, and P. S. Letelier, Phys. Rev. D 49, 5135 (1994).

    Article  ADS  Google Scholar 

  65. P. V. P. Cunha, N. A. Eiró, C. A. R. Herdeiro, and J. P. S. Lemos, J. Cosmol. Astropart. Phys. 2020, 035 (2020), ar**v: 1912.08833.

    Article  Google Scholar 

  66. Y. Tsunetoe, S. Mineshige, K. Ohsuga, T. Kawashima, and K. Akiyama, Publ. Astron. Soc. Jpn. 72, 32 (2020), ar**v: 2002.00954.

    Article  ADS  Google Scholar 

  67. Y. Tsunetoe, S. Mineshige, K. Ohsuga, T. Kawashima, and K. Akiyama, Publ. Astron. Soc. Jpn. 73, 912 (2021), ar**v: 2012.05243.

    Article  ADS  Google Scholar 

  68. E. Agol, Astrophys. J. 538, L121 (2000), ar**v: astro-ph/0005051.

    Article  ADS  Google Scholar 

  69. D. P. Marrone, J. M. Moran, J. H. Zhao, and R. Rao, Astrophys. J. 640, 308 (2006), ar**v: astro-ph/0511653.

    Article  ADS  Google Scholar 

  70. C. Y. Kuo, K. Asada, R. Rao, M. Nakamura, J. C. Algaba, H. B. Liu, M. Inoue, P. M. Koch, P. T. P. Ho, S. Matsushita, H. Y. Pu, K. Akiyama, H. Nishioka, and N. Pradel, Astrophys. J. 783, L33 (2014), ar**v: 1402.5238.

    Article  ADS  Google Scholar 

  71. J. P. Hamaker, and J. D. Bregman, Astron. Astrophys. Suppl. 117, 161 (1996).

    Article  ADS  Google Scholar 

  72. O. M. Smirnov, Astron. Astrophys. 527, A106 (2011), ar**v: 1101.1764.

    Article  ADS  Google Scholar 

  73. J. H. Krolik, J. F. Hawley, and S. Hirose, Astrophys. J. 622, 1008 (2005), ar**v: astro-ph/0409231.

    Article  ADS  Google Scholar 

  74. R. V. Shcherbakov, Astrophys. J. 688, 695 (2008), ar**v: 0809.0012.

    Article  ADS  Google Scholar 

  75. R. V. Shcherbakov, and L. Huang, Mon. Not. R. Astron. Soc. 410, 1052 (2011), ar**v: 1007.4831.

    Article  ADS  Google Scholar 

  76. J. Dexter, Mon. Not. R. Astron. Soc. 462, 115 (2016), ar**v: 1602.03184.

    Article  ADS  Google Scholar 

  77. A. K. Kulkarni, R. F. Penna, R. V. Shcherbakov, J. F. Steiner, R. Narayan, A. Sądowski, Y. Zhu, J. E. McClintock, S. W. Davis, and J. C. McKinney, Mon. Not. R. Astron. Soc. 414, 1183 (2011), ar**v: 1102.0010.

    Article  ADS  Google Scholar 

  78. M. Mościbrodzka, H. Falcke, and H. Shiokawa, Astron. Astrophys. 586, A38 (2016), ar**v: 1510.07243.

  79. M. Nakamura, K. Asada, K. Hada, H. Y. Pu, S. Noble, C. Tseng, K. Toma, M. Kino, H. Nagai, K. Takahashi, J. C. Algaba, M. Orienti, K. Akiyama, A. Doi, G. Giovannini, M. Giroletti, M. Honma, S. Koyama, R. Lico, K. Niinuma, and F. Tazaki, Astrophys. J. 868, 146 (2018), ar**v: 1810.09963.

    Article  ADS  Google Scholar 

  80. R. Narayan, et al. (The Event Horizon Telescope Collaboration), Astrophys. J. 912, 35 (2021), ar**v: 2105.01804.

    Article  ADS  Google Scholar 

  81. Z. Gelles, E. Himwich, M. D. Johnson, and D. C. M. Palumbo, Phys. Rev. D 104, 044060 (2021), ar**v: 2105.09440.

    Article  ADS  Google Scholar 

  82. M. Mosscibrodzka, J. Dexter, J. Davelaar, and H. Falcke, Mon. Not. R. Astron. Soc. 468, 2214 (2017), ar**v: 1703.02390.

    Article  ADS  Google Scholar 

  83. A. Eckart, R. Schödel, L. Meyer, S. Trippe, T. Ott, and R. Genzel, Astron. Astrophys. 455, 1 (2006), ar**v: astro-ph/0610103.

    Article  ADS  Google Scholar 

  84. S. Trippe, T. Paumard, T. Ott, S. Gillessen, F. Eisenhauer, F. Martins, and R. Genzel, Mon. Not. R. Astron. Soc. 375, 764 (2007), ar**v: astro-ph/0611737.

    Article  ADS  Google Scholar 

  85. M. Zamaninasab, A. Eckart, G. Witzel, M. Dovciak, V. Karas, R. Schödel, R. Gieübel, M. Bremer, M. García-Marín, D. Kunneriath, K. Mužić, S. Nishiyama, N. Sabha, C. Straubmeier, and A. Zensus, Astron. Astrophys. 510, A3 (2010), ar**v: 0911.4659.

    Article  Google Scholar 

  86. V. L. Fish, S. S. Doeleman, A. E. Broderick, A. Loeb, and A. E. E. Rogers, Astrophys. J. 706, 1353 (2009), ar**v: 0910.3893.

    Article  ADS  Google Scholar 

  87. A. E. Broderick, and A. Loeb, Mon. Not. R. Astron. Soc. 367, 905 (2006), ar**v: astro-ph/0509237.

    Article  ADS  Google Scholar 

  88. A. E. Broderick, and A. Loeb, Mon. Not. R. Astron. Soc. 363, 353 (2005), ar**v: astro-ph/0506433.

    Article  ADS  Google Scholar 

  89. X. Qin, S. Chen, and J. **g, Eur. Phys. J. C 82, 784 (2022), ar**v: 2111.10138.

    Article  ADS  Google Scholar 

  90. H. Zhu, and M. Guo, ar**v: 2205.04777.

  91. V. Delijski, G. Gyulchev, P. Nedkova, and S. Yazadjiev, ar**v: 2206.09455.

  92. X. Qin, S. Chen, Z. Zhang, and J. **g, Astrophys. J. 938, 2 (2022), ar**v: 2207.12034.

    Article  ADS  Google Scholar 

  93. X. Liu, S. Chen, and J. **g, ar**v: 2205.00391.

  94. M. Walker, and R. Penrose, Commun. Math. Phys. 18, 265 (1970).

    Article  ADS  Google Scholar 

  95. E. Himwich, M. D. Johnson, A. Lupsasca, and A. Strominger, Phys. Rev. D 101, 084020 (2020), ar**v: 2001.08750.

    Article  ADS  MathSciNet  Google Scholar 

  96. W. B. Bonnor, Z. Physik 190, 444 (1966).

    Article  ADS  MathSciNet  Google Scholar 

  97. Z. Zhang, S. Chen, and J. **g, Eur. Phys. J. C 82, 835 (2022), ar**v: 2205.13696.

    Article  ADS  Google Scholar 

  98. E. F. Boero, and O. M. Moreschi, Mon. Not. R. Astron. Soc. 507, 5974 (2021), ar**v: 2105.07075.

    Article  ADS  Google Scholar 

  99. M. Wang, S. Chen, and J. **g, Phys. Rev. D 104, 084021 (2021), ar**v: 2104.12304.

    Article  ADS  Google Scholar 

  100. H. C. D. Lima Jr, P. V. P. Cunha, C. A. R. Herdeiro, and L. C. B. Crispino, Phys. Rev. D 104, 044018 (2021), ar**v: 2104.09577.

    Article  ADS  Google Scholar 

  101. Y. Hou, Z. Zhang, H. Yan, M. Guo, and B. Chen, Phys. Rev. D 106, 064058 (2022), ar**v: 2206.13744.

    Article  ADS  Google Scholar 

  102. V. Perlick, O. Y. Tsupko, and G. S. Bisnovatyi-Kogan, Phys. Rev. D 92, 104031 (2015), ar**v: 1507.04217.

    Article  ADS  MathSciNet  Google Scholar 

  103. F. Atamurotov, B. Ahmedov, and A. Abdujabbarov, Phys. Rev. D 92, 084005 (2015), ar**v: 1507.08131.

    Article  ADS  Google Scholar 

  104. A. Abdujabbarov, B. Juraev, B. Ahmedov, and Z. Stuchlík, Astrophys. Space Sci. 361, 226 (2016).

    Article  ADS  Google Scholar 

  105. G. Crisnejo, and E. Gallo, Phys. Rev. D 97, 124016 (2018), ar**v: 1804.05473.

    Article  ADS  MathSciNet  Google Scholar 

  106. Y. Huang, Y. P. Dong, and D. J. Liu, Int. J. Mod. Phys. D 27, 1850114 (2018), ar**v: 1807.06268.

    Article  ADS  Google Scholar 

  107. H. Yan, Phys. Rev. D 99, 084050 (2019), ar**v: 1903.04382.

    Article  ADS  MathSciNet  Google Scholar 

  108. G. Z. Babar, A. Z. Babar, and F. Atamurotov, Eur. Phys. J. C 80, 761 (2020), ar**v: 2008.05845.

    Article  ADS  Google Scholar 

  109. K. Matsuno, Phys. Rev. D 103, 044008 (2021), ar**v: 2011.07742.

    Article  ADS  Google Scholar 

  110. O. Y. Tsupko, Phys. Rev. D 103, 104019 (2021), ar**v: 2102.00553.

    Article  ADS  MathSciNet  Google Scholar 

  111. Q. Li, Y. Zhu, and T. Wang, Eur. Phys. J. C 82, 2 (2022), ar**v: 2102.00957.

    Article  ADS  Google Scholar 

  112. F. Atamurotov, K. Jusufi, M. Jamil, A. Abdujabbarov, and M. Azreg-Aïnou, Phys. Rev. D 104, 064053 (2021), ar**v: 2109.08150.

    Article  ADS  Google Scholar 

  113. H. M. Wang, and S. W. Wei, Eur. Phys. J. Plus 137, 571 (2022), ar**v: 2106.14602.

    Article  Google Scholar 

  114. J. Badía, and E. F. Eiroa, Phys. Rev. D 104, 084055 (2021), ar**v: 2106.07601.

    Article  ADS  Google Scholar 

  115. Z. Zhang, H. Yan, M. Guo, and B. Chen (2022), ar**v: 2206.04430.

  116. F. Atamurotov, A. Abdujabbarov, and W. B. Han, Phys. Rev. D 104, 084015 (2021).

    Article  ADS  Google Scholar 

  117. V. Perlick, and O. Y. Tsupko, Phys. Rev. D 95, 104003 (2017), ar**v: 1702.08768.

    Article  ADS  MathSciNet  Google Scholar 

  118. V. Perlick, O. Y. Tsupko, and G. S. Bisnovatyi-Kogan, Phys. Rev. D 92, 104031 (2015), ar**v: 1507.04217.

    Article  ADS  MathSciNet  Google Scholar 

  119. B. Bezdĕková, V. Perlick, and J. Bičák, J. Math. Phys. 63, 092501 (2022), ar**v: 2204.05593.

    Article  ADS  Google Scholar 

  120. K. Hioki, and K. I. Maeda, Phys. Rev. D 80, 024042 (2009), ar**v: 0904.3575.

    Article  ADS  Google Scholar 

  121. S. W. Wei, Y. C. Zou, Y. X. Liu, and R. B. Mann, J. Cosmol. Astropart. Phys. 2019, 030 (2019), ar**v: 1904.07710.

    Article  Google Scholar 

  122. S. W. Wei, Y. X. Liu, and R. B. Mann, Phys. Rev. D 99, 041303 (2019), ar**v: 1811.00047.

    Article  ADS  Google Scholar 

  123. P. V. P. Cunha, and C. A. R. Herdeiro, Phys. Rev. Lett. 124, 181101 (2020), ar**v: 2003.06445.

    Article  ADS  MathSciNet  Google Scholar 

  124. A. A. Abdujabbarov, L. Rezzolla, and B. J. Ahmedov, Mon. Not. R. Astron. Soc. 454, 2423 (2015), ar**v: 1503.09054.

    Article  ADS  Google Scholar 

  125. D. Psaltis, F. Ozel, C. K. Chan, and D. P. Marrone, Astrophys. J. 814, 115 (2015), ar**v: 1411.1454.

    Article  ADS  Google Scholar 

  126. D. Marr, and E. Hildreth, Proc. R. Soc. Lon. Ser. B 207, 187 (1980).

    Article  ADS  Google Scholar 

  127. J. F. Canny, Finding Edges and Lines in Images, Technical Report (Massachusetts Institute of Technology, 1983).

  128. A. E. Broderick, T. Johannsen, A. Loeb, and D. Psaltis, Astrophys. J. 784, 7 (2014), ar**v: 1311.5564.

    Article  ADS  Google Scholar 

  129. K. Gebhardt, J. Adams, D. Richstone, T. R. Lauer, S. M. Faber, K. Gültekin, J. Murphy, and S. Tremaine, Astrophys. J. 729, 119 (2011), ar**v: 1101.1954.

    Article  ADS  Google Scholar 

  130. J. L. Walsh, A. J. Barth, L. C. Ho, and M. Sarzi, Astrophys. J. 770, 86 (2013), ar**v: 1304.7273.

    Article  ADS  Google Scholar 

  131. J. Kormendy, and L. C. Ho, Annu. Rev. Astron. Astrophys. 51, 511 (2013).

    Article  ADS  Google Scholar 

  132. D. Psaltis, et al. (EHT Collaboration), Phys. Rev. Lett. 125, 141104 (2020), ar**v: 2010.01055.

    Article  ADS  Google Scholar 

  133. T. Johannsen, Phys. Rev. D 87, 124017 (2013), ar**v: 1304.7786.

    Article  ADS  Google Scholar 

  134. J. Gair, and N. Yunes, Phys. Rev. D 84, 064016 (2011), ar**v: 1106.6313.

    Article  ADS  Google Scholar 

  135. R. Konoplya, L. Rezzolla, and A. Zhidenko, Phys. Rev. D 93, 064015 (2016), ar**v: 1602.02378.

    Article  ADS  MathSciNet  Google Scholar 

  136. P. Kocherlakota, et al. (EHT Collaboration), Phys. Rev. D 103, 104047 (2021), ar**v: 2105.09343.

    Article  ADS  Google Scholar 

  137. X. M. Kuang, Z. Y. Tang, B. Wang, and A. Wang, Phys. Rev. D 106, 064012 (2022), ar**v: 2206.05878.

    Article  ADS  Google Scholar 

  138. C. Bambi, and K. Freese, Phys. Rev. D 79, 043002 (2009), ar**v: 0812.1328.

    Article  ADS  MathSciNet  Google Scholar 

  139. Y. Mizuno, Z. Younsi, C. M. Fromm, O. Porth, M. De Laurentis, H. Olivares, H. Falcke, M. Kramer, and L. Rezzolla, Nat. Astron. 2, 585 (2018), ar**v: 1804.05812.

    Article  ADS  Google Scholar 

  140. P. V. P. Cunha, C. A. R. Herdeiro, and E. Radu, Phys. Rev. Lett. 123, 011101 (2019), ar**v: 1904.09997.

    Article  ADS  Google Scholar 

  141. B. P. Abbott, et al. (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. Lett. 116, 061102 (2016), ar**v: 1602.03837.

    Article  ADS  MathSciNet  Google Scholar 

  142. B. P. Abbott, et al. (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. Lett. 116, 241103 (2016), ar**v: 1606.04855.

    Article  ADS  Google Scholar 

  143. B. P. Abbott, et al. (LIGO Scientific and Virgo Collaboration), Phys. Rev. Lett. 118, 221101 (2017), ar**v: 1706.01812.

    Article  ADS  Google Scholar 

  144. B. P. Abbott, et al. (LIGO Scientific and Virgo Collaboration), Phys. Rev. Lett. 119, 141101 (2017), ar**v: 1709.09660.

    Article  ADS  Google Scholar 

  145. B. P. Abbott, et al. (LIGO Scientific and Virgo Collaboration), Astrophys. J. 851, L35 (2017), ar**v: 1711.05578.

    Article  ADS  Google Scholar 

  146. D. Nitta, T. Chiba, and N. Sugiyama, Phys. Rev. D 84, 063008 (2011), ar**v: 1106.2425.

    Article  ADS  Google Scholar 

  147. A. Yumoto, D. Nitta, T. Chiba, and N. Sugiyama, Phys. Rev. D 86, 103001 (2012), ar**v: 1208.0635.

    Article  ADS  Google Scholar 

  148. K. Okabayashi, N. Asaka, and K. Nakao, Phys. Rev. D 102, 044011 (2020), ar**v: 2003.07519.

    Article  ADS  MathSciNet  Google Scholar 

  149. J. O. Shipley, and S. R. Dolan, Class. Quantum Grav. 33, 175001 (2016), ar**v: 1603.04469.

    Article  ADS  Google Scholar 

  150. P. V. P. Cunha, C. A. R. Herdeiro, and M. J. Rodriguez, Phys. Rev. D 98, 044053 (2018), ar**v: 1805.03798.

    Article  ADS  MathSciNet  Google Scholar 

  151. T. Hertog, T. Lemmens, and B. Vercnocke, Phys. Rev. D 100, 046011 (2019), ar**v: 1903.05125.

    Article  ADS  MathSciNet  Google Scholar 

  152. R. A. Konoplya, Phys. Lett. B 795, 1 (2019), ar**v: 1905.00064.

    Article  ADS  MathSciNet  Google Scholar 

  153. X. Hou, Z. Xu, M. Zhou, and J. Wang, J. Cosmol. Astropart. Phys. 2018, 15 (2018), ar**v: 1804.08110.

    Article  Google Scholar 

  154. Z. Xu, X. Hou, X. Gong, and J. Wang, J. Cosmol. Astropart. Phys. 2018, 38 (2018), ar**v: 1803.00767.

    Article  Google Scholar 

  155. K. Jusufi, M. Jamil, and T. Zhu, Eur. Phys. J. C 80, 354 (2020), ar**v: 2005.05299.

    Article  ADS  Google Scholar 

  156. K. Jusufi, M. Jamil, P. Salucci, T. Zhu, and S. Haroon, Phys. Rev. D 100, 044012 (2019), ar**v: 1905.11803.

    Article  ADS  Google Scholar 

  157. P. V. P. Cunha, C. A. R. Herdeiro, and E. Radu, Universe 5, 220 (2019), ar**v: 1909.08039.

    Article  ADS  Google Scholar 

  158. N. S. Kardashev, et al. (RadioAstron Collaboration), Astron. Rep. 57, 153 (2013), ar**v: 1303.5013.

    Article  ADS  Google Scholar 

  159. R. D. Peccei, and H. R. Quinn, Phys. Rev. Lett. 38, 1440 (1977).

  160. S. Weinberg, Phys. Rev. Lett. 40, 223 (1978).

    Article  ADS  Google Scholar 

  161. F. Wilczek, Phys. Rev. Lett. 40, 279 (1978).

    Article  ADS  Google Scholar 

  162. L. Di Luzio, M. Giannotti, E. Nardi, and L. Visinelli, Phys. Rep. 870, 1 (2020).

    ADS  MathSciNet  Google Scholar 

  163. D. J. E. Marsh, Phys. Rep. 643, 1 (2016), ar**v: 1510.07633.

    Article  ADS  MathSciNet  Google Scholar 

  164. P. Sikivie, Rev. Mod. Phys. 93, 015004 (2021), ar**v: 2003.02206.

    Article  ADS  MathSciNet  Google Scholar 

  165. G. G. Raffelt, Lect. Notes Phys. 741, 51 (2008).

    Article  ADS  Google Scholar 

  166. G. G. Raffelt, Phys. Rep. 198, 1 (1990).

    Article  ADS  Google Scholar 

  167. V. Anastassopoulos, et al. (CAST Collaboration), Nat. Phys. 13, 584 (2017).

    Article  Google Scholar 

  168. A. Payez, C. Evoli, T. Fischer, M. Giannotti, A. Mirizzi, and A. Ringwald, J. Cosmol. Astropart. Phys. 2015(2), 6 (2015), ar**v: 1410.3747.

    Article  Google Scholar 

  169. M. J. Strafuss, and G. Khanna, Phys. Rev. D 71, 024034 (2005), ar**v: gr-qc/0412023.

    Article  ADS  MathSciNet  Google Scholar 

  170. R. Brito, V. Cardoso, and P. Pani, Lect. Notes Phys. 906, 1 (2015).

    Article  Google Scholar 

  171. S. M. Carroll, G. B. Field, and R. Jackiw, Phys. Rev. D 41, 1231 (1990).

    Article  ADS  Google Scholar 

  172. A. D. Plascencia, and A. Urbano, J. Cosmol. Astropart. Phys. 2018, 059 (2018), ar**v: 1711.08298.

    Article  Google Scholar 

  173. T. Fujita, R. Tazaki, and K. Toma, Phys. Rev. Lett. 122, 191101 (2019), ar**v: 1811.03525.

    Article  ADS  Google Scholar 

  174. M. A. Fedderke, P. W. Graham, and S. Rajendran, Phys. Rev. D 100, 015040 (2019), ar**v: 1903.02666.

    Article  ADS  Google Scholar 

  175. Y. Chen, J. Shu, X. Xue, Q. Yuan, and Y. Zhao, Phys. Rev. Lett. 124, 061102 (2020), ar**v: 1905.02213.

    Article  ADS  Google Scholar 

  176. A. Arvanitaki, M. Baryakhtar, and X. Huang, Phys. Rev. D 91, 084011 (2015), ar**v: 1411.2263.

    Article  ADS  Google Scholar 

  177. S. Shakeri, and F. Hajkarim, ar**v: 2209.13572.

  178. B. P. Singh, and S. G. Ghosh, Ann. Phys. 395, 127 (2018), ar**v: 1707.07125.

    Article  ADS  Google Scholar 

  179. U. Papnoi, F. Atamurotov, S. G. Ghosh, and B. Ahmedov, Phys. Rev. D 90, 024073 (2014), ar**v: 1407.0834.

    Article  ADS  Google Scholar 

  180. M. Amir, B. P. Singh, and S. G. Ghosh, Eur. Phys. J. C 78, 399 (2018), ar**v: 1707.09521.

    Article  ADS  Google Scholar 

  181. S. Vagnozzi, and L. Visinelli, Phys. Rev. D 100, 024020 (2019), ar**v: 1905.12421.

    Article  ADS  Google Scholar 

  182. L. Visinelli, N. Bolis, and S. Vagnozzi, Phys. Rev. D 97, 064039 (2018), ar**v: 1711.06628.

    Article  ADS  Google Scholar 

  183. J. C. S. Neves, Eur. Phys. J. C 80, 717 (2020), ar**v: 2005.00483.

    Article  ADS  Google Scholar 

  184. C. G. Böhmer, T. Harko, and F. S. N. Lobo, Class. Quantum Grav. 25, 045015 (2008), ar**v: 0801.1375.

    Article  ADS  Google Scholar 

  185. A. Y. Bin-Nun, Phys. Rev. D 82, 064009 (2010), ar**v: 1004.0379.

    Article  ADS  Google Scholar 

  186. A. F. Zakharov, Eur. Phys. J. C 78, 689 (2018), ar**v: 1804.10374.

    Article  ADS  Google Scholar 

  187. Z. Horvásth, and L. Á. Gergely, Astron. Nachr. 334, 1047 (2013), ar**v: 1203.6576.

    Article  ADS  Google Scholar 

  188. I. Banerjee, S. Chakraborty, and S. SenGupta, Phys. Rev. D 101, 041301 (2020), ar**v: 1909.09385.

    Article  ADS  Google Scholar 

  189. Z.-Y. Tang, X.-M. Kuang, B. Wang, and W.-L. Qian, ar**v: 2206.08608.

  190. F. Long, J. Wang, S. Chen, and J. **g, J. High Energ. Phys. 2019, 269 (2019).

    Article  ADS  Google Scholar 

  191. T. Wang, Nucl. Phys. B 756, 86 (2006), ar**v: hep-th/0605048.

    Article  ADS  Google Scholar 

  192. I. T. Drummond, and S. J. Hathrell, Phys. Rev. D 22, 343 (1980).

    Article  ADS  MathSciNet  Google Scholar 

  193. F. W. Hehl, and Y. N. Obukhov, Lect. Notes Phys. 562, 479 (1999).

    Article  ADS  Google Scholar 

  194. A. B. Balakin, V. V. Bochkarev, and J. P. S. Lemos, Phys. Rev. D 77, 084013 (2008), ar**v: 0712.4066.

    Article  ADS  Google Scholar 

  195. T. E. Clarke, P. P. Kronberg, and H. Böhringer, Astrophys. J. 547, L111 (2001), ar**v: astro-ph/0011281.

  196. K. Bamba, and S. D. Odintsov, J. Cosmol. Astropart. Phys. 2008, 24 (2008), ar**v: 0801.0954.

    Article  Google Scholar 

  197. Y. Huang, S. Chen, and J. **g, Eur. Phys. J. C 76, 594 (2016), ar**v: 1606.04634.

    Article  ADS  Google Scholar 

  198. Z. Zhang, S. Chen, X. Qin, and J. **g, Eur. Phys. J. C 81, 991 (2021), ar**v: 2106.07981.

    Article  ADS  Google Scholar 

  199. Z. Hu, Z. Zhong, P. C. Li, M. Guo, and B. Chen, Phys. Rev. D 103, 044057 (2021), ar**v: 2012.07022.

    Article  ADS  Google Scholar 

  200. S. F. Yan, C. Li, L. Xue, X. Ren, Y. F. Cai, D. A. Easson, Y. F. Yuan, and H. Zhao, Phys. Rev. Res. 2, 023164 (2020), ar**v: 1912.12629.

    Article  Google Scholar 

  201. L. Blackburn, S. Doeleman, J. Dexter, J. L. Gmez, M. D. Johnson, D. C. Palumbo, J. Weintroub, K. L. Bouman, A. A. Chael, J. R. Farah, V. Fish, L. Loinard, C. Lonsdale, G. Narayanan, N. A. Patel, D. W. Pesce, A. Raymond, R. Tilanus, M. Wielgus, K. Akiyama, G. Bower, A. Broderick, R. Deane, C. M. Fromm, C. Gammie, R. Gold, M. Janssen, T. Kawashima, T. Krichbaum, D. P. Marrone, L. D. Matthews, Y. Mizuno, L. Rezzolla, F. Roelofs, E. Ros, T. K. Savolainen, F. Yuan, and G. Zhao, ar**v: 1909.01411.

  202. J. C. S. Neves, Eur. Phys. J. C 80, 343 (2020), ar**v: 1906.11735.

    Article  ADS  Google Scholar 

  203. M. Khodadi, and G. Lambiase, Phys. Rev. D 106, 104050 (2022), ar**v: 2206.08601.

    Article  ADS  Google Scholar 

  204. S. Vagnozzi, R. Roy, Y.-D. Tsai, L. Visinelli, M. Afrin, A. Allahyari, P. Bambhaniya, D. Dey, S. G. Ghosh, P. S. Joshi, K. Jusufi, M. Khodadi, R. K. Walia, A. Övgün, and C. Bambi, ar**v: 2205.07787.

  205. F. Özel, D. Psaltis, and Z. Younsi, Astrophys. J. 941, 88 (2022), ar**v: 2111.01123.

    Article  ADS  Google Scholar 

  206. D. Psaltis, Gen. Relativ. Gravit. 51, 137 (2019), ar**v: 1806.09740.

    Article  ADS  MathSciNet  Google Scholar 

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Correspondence to Songbai Chen.

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This work was supported by the National Natural Science Foundation of China (Grant Nos. 12035005, 12275078, and 11875026). We would like to thank Profs. Carlos Herdeiro and Jieci Wang for their useful comments and suggestions.

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Chen, S., **g, J., Qian, WL. et al. Black hole images: A review. Sci. China Phys. Mech. Astron. 66, 260401 (2023). https://doi.org/10.1007/s11433-022-2059-5

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