- 
								[1]
								J. P. Luminet, Astron. Astrophys. 75, 228-235 (1979) 
- 
								[2]
								P. V. P. Cunha, N. A. Eiró, C. A. R. Herdeiro et al., JCAP 03, 035 (2020) 
- 
								[3]
								R. Narayan, M. D. Johnson, and C. F. Gammie, Astrophys. J. Lett. 885(2), L33 (2019) 
- 
								[4]
								K. Akiyama et al. (Event Horizon Telescope), Astrophys. J. Lett. 875, L1 (2019) 
- 
								[5]
								K. Akiyama et al. (Event Horizon Telescope), Astrophys. J. Lett. 875(1), L2 (2019) 
- 
								[6]
								K. Akiyama et al. (Event Horizon Telescope), Astrophys. J. Lett. 875(1), L3 (2019) 
- 
								[7]
								K. Akiyama et al. (Event Horizon Telescope), Astrophys. J. Lett. 875(1), L4 (2019) 
- 
								[8]
								K. Akiyama et al. (Event Horizon Telescope), Astrophys. J. Lett. 875(1), L5 (2019) 
- 
								[9]
								K. Akiyama et al. (Event Horizon Telescope), Astrophys. J. Lett. 875(1), L6 (2019) 
- 
								[10]
								Y. Mizuno, Z. Younsi, C. M. Fromm et al., Nature Astron. 2(7), 585-590 (2018) 
- 
								[11]
								J. L. Synge, Mon. Not. Roy. Astron. Soc. 131(3), 463-466 (1966) 
- 
								[12]
								J. M. Bardeen, W. H. Press, and S. A. Teukolsky, Astrophys. J. 178, 347 (1972) 
- 
								[13]
								S. E. Gralla, D. E. Holz, and R. M. Wald, Phys. Rev. D 100(2), 024018 (2019) 
- 
								[14]
								S. E. Gralla and A. Lupsasca, Phys. Rev. D 101(4), 044031 (2020) 
- 
								[15]
								J. Peng, M. Guo, and X. H. Feng, Chin. Phys. C 45(8), 085103 (2021) 
- 
								[16]
								J. Peng, M. Guo, and X. H. Feng, Phys. Rev. D 104(12), 124010 (2021) 
- 
								[17]
								P. V. P. Cunha, C. A. R. Herdeiro, E. Radu et al., Phys. Rev. Lett. 115(21), 211102 (2015) 
- 
								[18]
								J. Grover, J. Kunz, P. Nedkova et al., Phys. Rev. D 97(8), 084024 (2018) 
- 
								[19]
								A. Yumoto, D. Nitta, T. Chiba et al., Phys. Rev. D 86, 103001 (2012) 
- 
								[20]
								L. Amarilla, E. F. Eiroa, and G. Giribet, Phys. Rev. D 81, 124045 (2010) 
- 
								[21]
								R. Kumar, B. P. Singh, M. S. Ali et al., Phys. Dark Univ. 34, 100881 (2021) 
- 
								[22]
								J. R. Mureika and G. U. Varieschi, Can. J. Phys. 95(12), 1299-1306 (2017) 
- 
								[23]
								V. Perlick and O. Y. Tsupko, Phys. Rev. D 95(10), 104003 (2017) 
- 
								[24]
								P. V. P. Cunha and C. A. R. Herdeiro, Gen. Rel. Grav. 50(4), 42 (2018) 
- 
								[25]
								R. A. Konoplya, Phys. Lett. B 795, 1-6 (2019) 
- 
								[26]
								K. Hioki and K. i. Maeda, Phys. Rev. D 80, 024042 (2009) 
- 
								[27]
								N. Tsukamoto, Phys. Rev. D 97(6), 064021 (2018) 
- 
								[28]
								R. Takahashi, Publ. Astron. Soc. Jap. 57, 273 (2005) 
- 
								[29]
								Q. Gan, P. Wang, H. Wu et al., Phys. Rev. D 104(4), 044049 (2021) 
- 
								[30]
								S. W. Wei and Y. X. Liu, JCAP 11, 063 (2013) 
- 
								[31]
								A. Abdujabbarov, F. Atamurotov, Y. Kucukakca et al., Astrophys. Space Sci. 344, 429-435 (2013) 
- 
								[32]
								J. Podolsky and R. Svarc, Phys. Rev. D 85, 044057 (2012) 
- 
								[33]
								J. Schee and Z. Stuchlik, Int. J. Mod. Phys. D 18, 983-1024 (2009) 
- 
								[34]
								C. Bambi, F. Caravelli, and L. Modesto, Phys. Lett. B 711, 10-14 (2012) 
- 
								[35]
								C. Bambi and N. Yoshida, Class. Quant. Grav. 27, 205006 (2010) 
- 
								[36]
								Z. Younsi, A. Zhidenko, L. Rezzolla et al., Phys. Rev. D 94(8), 084025 (2016) 
- 
								[37]
								P. V. P. Cunha, C. A. R. Herdeiro, B. Kleihaus et al., Phys. Lett. B 768, 373-379 (2017) 
- 
								[38]
								A. Belhaj, H. Belmahi, and M. Benali, Phys. Lett. B 821, 136619 (2021) 
- 
								[39]
								A. Abdujabbarov, M. Amir, B. Ahmedov et al., Phys. Rev. D 93(10), 104004 (2016) 
- 
								[40]
								M. Amir and S. G. Ghosh, Phys. Rev. D 94(2), 024054 (2016) 
- 
								[41]
								A. Saha, S. M. Modumudi, and S. Gangopadhyay, Gen. Rel. Grav. 50(8), 103 (2018) 
- 
								[42]
								E. F. Eiroa and C. M. Sendra, Eur. Phys. J. C 78(2), 91 (2018) 
- 
								[43]
								G. Lara, S. H. Völkel, and E. Barausse, Phys. Rev. D 104(12), 124041 (2021) 
- 
								[44]
								A. C. Pope et al. (SDSS), Astrophys. J. 607, 655-660 (2004) 
- 
								[45]
								E. Komatsu et al. (WMAP), Astrophys. J. Suppl. 192, 18 (2011) 
- 
								[46]
								V. V. Kiselev, Class. Quant. Grav. 20, 1187-1198 (2003) 
- 
								[47]
								E. J. Copeland, M. Sami, and S. Tsujikawa, Int. J. Mod. Phys. D 15, 1753-1936 (2006) 
- 
								[48]
								S. Perlmutter et al. (Supernova Cosmology Project), Astrophys. J. 517, 565-586 (1999) 
- 
								[49]
								A. G. Riess et al. (Supernova Search Team), Astron. J. 116, 1009-1038 (1998) 
- 
								[50]
								P. M. Garnavich et al. (Supernova Search Team), Astrophys. J. 509, 74-79 (1998) 
- 
								[51]
								S. Vagnozzi, C. Bambi, and L. Visinelli, Class. Quant. Grav. 37(8), 087001 (2020) 
- 
								[52]
								B. Stern, Y. Tikhomirova, M. Stepanov et al., Astrophys. J. Lett. 540, L21 (2000) 
- 
								[53]
								N. A. Bahcall, J. P. Ostriker, S. Perlmutter et al., Science 284, 1481-1488 (1999) 
- 
								[54]
								P. J. Steinhardt, L. M. Wang, and I. Zlatev, Phys. Rev. D 59, 123504 (1999) 
- 
								[55]
								L. M. Wang, R. R. Caldwell, J. P. Ostriker et al., Astrophys. J. 530, 17-35 (2000) 
- 
								[56]
								E. Frion, L. Giani, and T. Miranda, Open J.Astrophys. 4, 1 (2021) 
- 
								[57]
								C. H. Nam, Gen. Rel. Grav. 52(1), 1 (2020) 
- 
								[58]
								X. X. Zeng and H. Q. Zhang, Eur. Phys. J. C 80(11), 1058 (2020) 
- 
								[59]
								S. U. Khan and J. Ren, Phys. Dark Univ. 30, 100644 (2020) 
- 
								[60]
								P. S. Letelier, Phys. Rev. D 20, 1294-1302 (1979) 
- 
								[61]
								P. S. Letelier, Phys. Rev. D 28, 2414-2419 (1983) 
- 
								[62]
								D. Barbosa and V. B. Bezerra, Gen. Rel. Grav. 48(11), 149 (2016) 
- 
								[63]
								J. M. Toledo and V. B. Bezerra, Gen. Rel. Grav. 52(4), 34 (2020) 
- 
								[64]
								E. Herscovich and M. G. Richarte, Phys. Lett. B 689, 192-200 (2010) 
- 
								[65]
								J. M. Toledo and V. B. Bezerra, Eur. Phys. J. C 79(2), 117 (2019) 
- 
								[66]
								X. C. Cai and Y. G. Miao, Phys. Rev. D 101(10), 104023 (2020) 
- 
								[67]
								M. Chabab and S. Iraoui, Gen. Rel. Grav. 52(8), 75 (2020) 
- 
								[68]
								J. M. Toledo and V. B. Bezerra, Eur. Phys. J. C 79(2), 110 (2019) 
- 
								[69]
								J. de M.Toledo and V. B. Bezerra, Eur. Phys. J. C 78(7), 534 (2018) 
- 
								[70]
								J. L. Friedman, K. Schleich, and D. M. Witt, Phys. Rev. Lett. 71(10), 1486-1489 (1993) 
- 
								[71]
								G. J. Galloway, Classical Quantum Gravity 12(10), L99-L101 (1995) 
- 
								[72]
								X. X. Zeng, H. Q. Zhang, and H. Zhang, Eur. Phys. J. C 80(9), 872 (2020) 
- 
								[73]
								E. Teo, Gen. Rel. Grav. 53(1), 10 (2021) 
- 
								[74]
								M. Jaroszynski and A. Kurpiewski, Astron. Astrophys. 326, 419 (1997) 
- 
								[75]
								C. Bambi, Phys. Rev. D 87, 107501 (2013) 
- 
								[76]
								Z. Hu, Z. Zhong, P. C. Li et al., Phys. Rev. D 103(4), 044057 (2021) 
- 
								[77]
								H. Lu and H. D. Lyu, Phys. Rev. D 101(4), 044059 (2020) 
- 
								[78]
								M. Guo and P. C. Li, Eur. Phys. J. C 80(6), 588 (2020)