- 
								[1]
								H. R. Smart and A. S. Eddington, The Philosophical Review 31, 414 (1922) 
- 
								[2]
								O. Chwolson, Astronomische Nachrichten 221, 329 (1924) 
- 
								[3]
								A. Einstein, Science 84, 506 (1936) 
- 
								[4]
								M. Schmidt, Nature 197, 1040 (1963) 
- 
								[5]
								D. Walsh, R. F. Carswell, and R. J. Weymann, Nature 279, 381 (1979) 
- 
								[6]
								K. S. Virbhadra, (2022), arXiv: 2204.01792 
- 
								[7]
								C. Kochanek, Saas-Fee Advanced Course 33, 91 (2006) 
- 
								[8]
								D. Jauncey et al., Nature 352, 132 (1991) 
- 
								[9]
								P. V. P. Cunha, C. A. R. Herdeiro, and E. Radu, Phys. Rev. D 96, 024039 (2017), arXiv:1705.05461 
- 
								[10]
								P. V. P. Cunha and C. A. R. Herdeiro, Gen. Rel. Grav. 50, 42 (2018), arXiv:1801.00860 
- 
								[11]
								V. Perlick and O. Y. Tsupko, Phys. Rept. 947, 1 (2022), arXiv:2105.07101 
- 
								[12]
								S. Chen, J. Jing, W.-L. Qian et al., Sci. China Phys. Mech. Astron. 66, 260401 (2023), arXiv:2301.00113 
- 
								[13]
								K. Akiyama et al. (Event Horizon Telescope), Astrophys. J. Lett. 875, L4 (2019), arXiv:1906.11241 
- 
								[14]
								K. S. Virbhadra, Phys. Rev. D 106, 064038 (2022), arXiv:2204.01879 
- 
								[15]
								Z.-Y. Tang, X.-M. Kuang, B. Wang et al., Sci. Bull. 67, 2272 (2022), arXiv:2206.08608 
- 
								[16]
								X.-M. Kuang, Z.-Y. Tang, B. Wang et al., Phys. Rev. D 106, 064012 (2022), arXiv:2206.05878 
- 
								[17]
								Z.-Y. Tang, X.-M. Kuang, B. Wang et al., arXiv: 2211.08137 
- 
								[18]
								J. Sun, Y. Liu, W.-L. Qian et al., Chin. Phys. C 47, 025104 (2023) 
- 
								[19]
								J. Tang, Y. Liu, W.-L. Qian et al., Chin. Phys. C 47, 025105 (2023) 
- 
								[20]
								X.-J. Wang, X.-M. Kuang, Y. Meng et al., arXiv: 2304.10015 
- 
								[21]
								M.-H. Wu, H. Guo, and X.-M. Kuang, Phys. Rev. D 107, 064033 (2023) 
- 
								[22]
								Y. Meng, X.-M. Kuang, X.-J. Wang et al., Phys. Lett. B 841, 137940 (2023) 
- 
								[23]
								E. Ghorani et al., Eur. Phys. J. C 83, 318 (2023), arXiv:2304.03660 
- 
								[24]
								S. V. M. C. B. Xavier, H. C. D. Lima Junior, and L. C. B. Crispino, Phys. Rev. D 107, 064040 (2023), arXiv:2303.17666 
- 
								[25]
								W.-L. Qian, S. Chen, C.-G. Shao et al., Eur. Phys. J. C 82, 91 (2022), arXiv:2102.03820 
- 
								[26]
								Y. Hou, M. Guo, and B. Chen, Phys. Rev. D 104, 024001 (2021), arXiv:2103.04369 
- 
								[27]
								P. V. P. Cunha et al., Phys. Rev. D 94, 104023 (2016), arXiv:1609.01340 
- 
								[28]
								J. Shipley and S. R. Dolan, Class. Quant. Grav. 33, 175001 (2016), arXiv:1603.04469 
- 
								[29]
								U. Yurtsever, Phys. Rev. D 52, 3176 (1995), arXiv:gr-qc/9412031 
- 
								[30]
								M. Wang, S. Chen, and J. Jing, Phys. Rev. D 97, 064029 (2018), arXiv:1710.07172 
- 
								[31]
								M. Wang, S. Chen, and J. Jing, Phys. Rev. D 98, 104040 (2018), arXiv:1801.02118 
- 
								[32]
								V. Manko and I. Novikov, Classical and Quantum Gravity 9, 2477 (1992) 
- 
								[33]
								G. Lukes-Gerakopoulos, T. A. Apostolatos, and G. Contopoulos, Phys. Rev. D 81, 124005 (2010), arXiv:1003.3120 
- 
								[34]
								J. R. Gair, C. Li, and I. Mandel, Phys. Rev. D 77, 024035 (2008), arXiv:0708.0628 
- 
								[35]
								C. Bambi and E. Barausse, Astrophys. J. 731, 121 (2011), arXiv:1012.2007 
- 
								[36]
								K. Destounis and K. D. Kokkotas, Phys. Rev. D 104, 064023 (2021), arXiv:2108.02782 
- 
								[37]
								C. Herdeiro and E. Radu, Phys. Rev. D 89, 124018 (2014), arXiv:1406.1225 
- 
								[38]
								C. A. Herdeiro, E. Radu, and H. F. Rúnarsson, International Journal of Modern Physics D 25, 1641014 (2016), arXiv:1604.06202 
- 
								[39]
								N. Comins and B. F. Schutz, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 364, 211 (1978) 
- 
								[40]
								T. A. Jacobson and G. E. Volovik, Phys. Rev. D 58, 064021 (1998), arXiv:cond-mat/9801308 
- 
								[41]
								P. V. P. Cunha, C. A. R. Herdeiro, E. Radu et al., Int. J. Mod. Phys. D 25, 1641021 (2016), arXiv:1605.08293 
- 
								[42]
								T. Johannsen, Astrophys. J. 777, 170 (2013), arXiv:1501.02814 
- 
								[43]
								J. Pathak, B. Hunt, M. Girvan et al., Phys. Rev. Lett. 120, 024102 (2018), arXiv:2110.13614