- 
								[1]
								R. A. Konoplya and A. Zhidenko, Phys. Rev. Lett 128, 091104 (2022), arXiv:2106.05034[gr-qc 
- 
								[2]
								G. Mustafa, M. Ahmad, A. Övgün et al., Fortschritte der Physik 69, 2100048 (2021), arXiv:2104.13760[gr-qc 
- 
								[3]
								R. Avalos, E. Fuenmayor, and E. Contreras, Eur. Phys. J. C 82, 420 (2022), arXiv:2208.10261[gr-qc 
- 
								[4]
								C. A. Benavides-Gallego, W.-B. Han, D. Malafarina et al., Phys. Rev. D 104, 084024 (2021), arXiv:2107.07998[gr-qc 
- 
								[5]
								G. Bertone and D. Hooper, Rev. Mod. Phys. 90, 045002 (2018), arXiv:1605.04909[astroph.CO 
- 
								[6]
								D. Huterer and D. L. Shafer, Rep. Prog. Phys. 81, 016901 (2018), arXiv:1709.01091[astroph.CO 
- 
								[7]
								J. L. Synge, Mon. Not. Roy. Astron. Soc. 131, 463 (1966) 
- 
								[8]
								J. P. Luminet, Astron.Astrophys. 75, 228 (1979) 
- 
								[9]
								H. Falcke, F. Melia, and E. Agol, Astrophys. J. 528, L13 (2000), arXiv:astro-ph/9912263[astro-ph 
- 
								[10]
								V. Perlick and O. Y. Tsupko, Phys. Rep. 947, 1 (2022), arXiv:2105.07101[gr-qc 
- 
								[11]
								K. Hioki and K.-I. Maeda, Phys. Rev. D 80, 024042 (2009) 
- 
								[12]
								K. Akiyama and, et al, Astrophys. J. 875, L1 (2019), arXiv:1906.11238[astro-ph.GA 
- 
								[13]
								K. Akiyama and, et al, Astrophys. J. Lett 930, L12 (2022) 
- 
								[14]
								C. Bambi and K. Freese, Phys. Rev. D. 79, 043002 (2009), arXiv:0812.1328[astro-ph 
- 
								[15]
								L. Amarilla and E. F. Eiroa, Phys. Rev. D 85, 064019 (2012) 
- 
								[16]
								A. Abdujabbarov, M. Amir, B. Ahmedov et al., Phys. Rev. D 93, 104004 (2016), arXiv:1604.03809[gr-qc 
- 
								[17]
								F. Atamurotov, A. Abdujabbarov, and B. Ahmedov, Phys. Rev. D 88, 064004 (2013) 
- 
								[18]
								N. Tsukamoto, Phys. Rev. D. 97, 064021 (2018), arXiv:1708.07427[gr-qc 
- 
								[19]
								S.-W. Wei and Y.-X. Liu, Eur. Phys. J. Plus 136, 436 (2021), arXiv:2003.07769[gr-qc 
- 
								[20]
								X. Hou, Z. Xu, and J. Wang, J. Cosmol. A. P 2018, 040 (2018) 
- 
								[21]
								V. Perlick, O. Y. Tsupko, and G. S. Bisnovatyi-Kogan, Phys. Rev. D. 97, 104062 (2018), arXiv:1804.04898[gr-qc 
- 
								[22]
								P. V. P. Cunha, N. A. Eiró, C. A. R. Herdeiro et al., J. Cosmol. A. P 2020, 035 (2020), arXiv:1912.08833[gr-qc 
- 
								[23]
								M. Afrin, R. Kumar, and S. G. Ghosh, Parameter estimation of hairy Kerr black holes from its shadow and constraints from M87 *, Mon. Not. R. Astron. Soc. 504 (4), 5927 (2020), arXiv: 2103.11417[grqc 
- 
								[24]
								F. Atamurotov, S. G. Ghosh, and B. Ahmedov, Eur. Phys. J. C 76, 273 (2016), arXiv:1506.03690[gr-qc 
- 
								[25]
								F. Atamurotov, U. Papnoi, and K. Jusufi, Classical and Quantum Gravity 39, 025014 (2022), arXiv:2104.14898[gr-qc 
- 
								[26]
								F. Atamurotov, I. Hussain, G. Mustafa et al., Eur. Phys. J. C 82, 831 (2022), arXiv:2209.01652[gr-qc 
- 
								[27]
								F. Sarikulov, F. Atamurotov, A. Abdujabbarov et al., Eur. Phys. J. C 82, 771 (2022) 
- 
								[28]
								G. Mustafa, F. Atamurotov, I. Hussain et al., Chinese Physics C 46, 125107 (2022), arXiv:2207.07608[gr-qc 
- 
								[29]
								T. Ohgami and N. Sakai, Phys. Rev. D 91, 124020 (2015), arXiv:1704.07065[gr-qc 
- 
								[30]
								X. Wang, P.-C. Li, C.-Y. Zhang et al., Phys. Lett. B 811, 135930 (2020), arXiv:2007.03327[gr-qc 
- 
								[31]
								M. Wielgus, J. Horák, F. Vincent et al., Phys. Rev. D 102, 084044 (2020), arXiv:2008.10130[gr-qc 
- 
								[32]
								V. Perlick and O. Y. Tsupko, Phys. Rep. 947, 1 (2022), arXiv:2105.07101[gr-qc 
- 
								[33]
								K. A. Bronnikov, R. A. Konoplya, and T. D. Pappas, Phys. Rev. D 103, 124062 (2021), arXiv:2102.10679[gr-qc 
- 
								[34]
								K. Jusufi, S. Kumar, M. Azreg-Aïnou et al., Eur. Phys. J. C 82, 633 (2022), arXiv:2106.08070[gr-qc 
- 
								[35]
								A. Abdujabbarov, B. Juraev, B. Ahmedov et al., Astrophys. Space Sci. 361, 226 (2016) 
- 
								[36]
								S. Kumar, A. Uniyal, and S. Chakrabarti, Shadow and Weak Gravitational lensing of rotating traversable Wormhole in Non-homogeneous Plasma Spacetime, (2023), arXiv: 2308.05545[gr-qc 
- 
								[37]
								A. S. Eddington, The Observatory 42, 119 (1919) 
- 
								[38]
								R. Shaikh, P. Banerjee, S. Paul et al., Phys. Lett. B 789, 270 (2019), arXiv:1811.08245[gr-qc 
- 
								[39]
								M. A. Bugaev, I. D. Novikov, S. V. Repin et al., Astronomy Reports 65, 1185 (2021), arXiv:2106.03256[gr-qc 
- 
								[40]
								K. K. Nandi, Y.-Z. Zhang, and A. V. Zakharov, Phys. Rev. D 74, 024020 (2006), arXiv:gr-qc/0602062[gr-qc 
- 
								[41]
								T. Müller, Phys. Rev. D 77, 044043 (2008) 
- 
								[42]
								K. Nakajima and H. Asada, Phys. Rev. D 85, 107501 (2012), arXiv:1204.3710[gr-qc 
- 
								[43]
								C.-M. Yoo, T. Harada, and N. Tsukamoto, Phys. Rev. D 87, 084045 (2013), arXiv:1302.7170[gr-qc 
- 
								[44]
								N. Tsukamoto and T. Harada, Phys. Rev. D 95, 024030 (2017), arXiv:1607.01120[gr-qc 
- 
								[45]
								K. Jusufi and A. Ã-vgün, Phys. Rev. D 97, 024042 (2018), arXiv:1708.06725[gr-qc 
- 
								[46]
								Z. Li, G. He, and T. Zhou, Phys. Rev. D 101, 044001 (2020), arXiv:1908.01647[gr-qc 
- 
								[47]
								V. A. Ishkaeva and S. V. Sushkov, Image of an accreting general Ellis-Bronnikov wormhole, (2023), arXiv: 2308.02268[gr-qc 
- 
								[48]
								N. Tsukamoto, Phys. Rev. D 101, 104021 (2020), arXiv:2004.00822[gr-qc 
- 
								[49]
								G. S. Bisnovatyi-Kogan and O. Y. Tsupko, Mon. Not. R. Astron. Soc. 404, 1790 (2010) 
- 
								[50]
								A. Rogers, Mon. Not. R. Astron. Soc. 451, 17 (2015) 
- 
								[51]
								V. S. Morozova, B. J. Ahmedov, and A. A. Tursunov, Astrophys Space Sci 346, 513 (2013) 
- 
								[52]
								F. Atamurotov, A. Abdujabbarov, and W.-B. Han, Phys. Rev. D 104, 084015 (2021) 
- 
								[53]
								S. Hensh, A. Abdujabbarov, J. Schee et al., European Physical Journal C 79, 533 (2019), arXiv:1904.08776[gr-qc 
- 
								[54]
								G. Z. Babar, F. Atamurotov, Phys. Dark Universe 32, 100798 (2021) 
- 
								[55]
								W. Javed, I. Hussain, and A. Övgün, Eur. Phys. J. Plus 137, 148 (2022), arXiv:2201.09879[grqc 
- 
								[56]
								F. Atamurotov, S. Shaymatov, and P. Sheoran, J. Cosmol. A. P. 2021, 045 (2021), arXiv:2105.02214[gr-qc 
- 
								[57]
								F. Atamurotov, H. Alibekov, A. Abdujabbarov et al., Symmetry 15, 848 (2023) 
- 
								[58]
								F. Atamurotov, D. Ortiqboev, A. Abdujabbarov et al., Eur. Phys. J. C 82, 659 (2022) 
- 
								[59]
								S.-S. Zhao and Y. Xie, Phys. Lett. B. 774, 357 (2017) 
- 
								[60]
								F. Atamurotov and S. G. Ghosh, Eur. Phys. J. Plus 137, 662 (2022) 
- 
								[61]
								F. Atamurotov, M. Jamil, and K. Jusufi, Chin. Phys. C 47, 035106 (2023), arXiv:2212.12949[gr-qc 
- 
								[62]
								F. Atamurotov, I. Hussain, G. Mustafa et al., Chin. Phys. C 47, 025102 (2023) 
- 
								[63]
								F. Atamurotov, M. Alloqulov, A. Abdujabbarov et al., Eur. Phys. J. Plus 137, 634 (2022) 
- 
								[64]
								F. Atamurotov, F. Sarikulov, A. Abdujabbarov et al., Eur. Phys. J. Plus 137, 336 (2022) 
- 
								[65]
								F. Atamurotov, S. Shaymatov, and B. Ahmedov, Galaxies 9, 54 (2021) 
- 
								[66]
								F. Sarikulov, F. Atamurotov, A. Abdujabbarov et al., Chinese Physics C 47, 115101 (2023) 
- 
								[67]
								M. Alloqulov, F. Atamurotov, A. Abdujabbarov et al., Chinese Physics C 47, 075103 (2023) 
- 
								[68]
								C.-Y. Wang, Y.-F. Shen, and Y. Xie, JCAP (4), 022 (2019), arXiv:1902.03789[grqc 
- 
								[69]
								X. Lu and Y. Xie, Eur. Phys. J. C 79, 1016 (2019) 
- 
								[70]
								Y.-X. Gao and Y. Xie, Phys. Rev. D 103, 043008 (2021) 
- 
								[71]
								X. Lu and Y. Xie, Eur. Phys. J. C 81, 627 (2021) 
- 
								[72]
								J. Zhang and Y. Xie, Eur. Phys. J. C 82, 471 (2022), arXiv:2201.09703[gr-qc 
- 
								[73]
								X. Lu, F.-W. Yang, and Y. Xie, Eur. Phys. J. C 76, 357 (2016), arXiv:1606.02932[gr-qc 
- 
								[74]
								S.-S. Zhao and Y. Xie, Eur. Phys. J. C 77, 272 (2017), arXiv:1704.02434[gr-qc 
- 
								[75]
								X.-T. Cheng and Y. Xie, Phys. Rev. D 103, 064040 (2021) 
- 
								[76]
								Y. Xie and X.-M. Deng, MNRAS 433, 3584 (2013), arXiv:1312.4103[gr-qc 
- 
								[77]
								S.-S. Zhao and Y. Xie, Phys. Rev. D 92, 064033 (2015) 
- 
								[78]
								Z.-W. Li, S.-F. Yuan, C. Lu et al., Research in Astronomy and Astrophysics 14, 139 (2014) 
- 
								[79]
								X.-M. Deng and Y. Xie, Annals of Physics 361, 62 (2015) 
- 
								[80]
								H.-Y. Lin and X.-M. Deng, Annals of Physics 455, 169360 (2023) 
- 
								[81]
								J. Zhang and Y. Xie, Eur. Phys. J. C 82, 854 (2022) 
- 
								[82]
								B. Gao and X.-M. Deng, Eur. Phys. J. C 81, 983 (2021) 
- 
								[83]
								T.-Y. Zhou and Y. Xie, Eur. Phys. J. C 80, 1070 (2020) 
- 
								[84]
								H.-Y. Lin and X.-M. Deng, Eur. Phys. J. Plus 137, 176 (2022) 
- 
								[85]
								B. Gao and X.-M. Deng, Annals of Physics 418, 168194 (2020) 
- 
								[86]
								J. L. Synge, Relativity: The General Theory, (NorthHolland, Amsterdam, 1960) 
- 
								[87]
								O. Y. Tsupko and G. S. Bisnovatyi-Kogan, Gravit. Cosmol. 15, 184 (2009) 
- 
								[88]
								V. Perlick, O. Y. Tsupko, and G. S. Bisnovatyi-Kogan, Phys. Rev. D. 92, 104031 (2015), arXiv:1507.04217[gr-qc 
- 
								[89]
								F. Atamurotov, K. Jusufi, M. Jamil et al., Phys. Rev. D 104, 064053 (2021), arXiv:2109.08150[gr-qc 
- 
								[90]
								K. Akiyama and, et al, Astrophys. J. 910, L12 (2021) 
- 
								[91]
								F. Atamurotov, A. Abdujabbarov, and J. Rayimbaev, Eur. Phys. J. C. 81, 118 (2021) 
- 
								[92]
								V. Bozza, Phys. Rev. D 78, 103005 (2008), arXiv:0807.3872[gr-qc 
- 
								[93]
								Y. Wang, JCAP (3), 005 (2005), arXiv:astro-ph/0406635[astro-ph 
- 
								[94]
								E. J. Gonzalez, G. Föex, J. L. Nilo Castell′on et al., MNRAS 452, 2225 (2015), arXiv:1504.03364[astro-ph.CO 
- 
								[95]
								Z. Kalantari and S. Rahvar, The Astrophysical Journal 934, 106 (2022), arXiv:2205.05278[astro-ph.HE 
- 
								[96]
								D. Wen and A. J. Kemball, Testing Primordial Black Hole Dark Matter with ALMA Observations of the Gravitational Lens B1422+231, (2022), arXiv: 2210.16444[astroph.CO