• [1]

    The Event Horizon Telescope Collaboration, Astrophys. J. Lett. 875, L1 (2019)

  • [2]

    The Event Horizon Telescope Collaboration, Astrophys. J. Lett. 875, L2 (2019)

  • [3]

    The Event Horizon Telescope Collaboration, Astrophys. J. Lett. 875, L3 (2019)

  • [4]

    The Event Horizon Telescope Collaboration, Astrophys. J. Lett. 875, L4 (2019)

  • [5]

    The Event Horizon Telescope Collaboration, Astrophys. J. Lett. 875, L5 (2019)

  • [6]

    The Event Horizon Telescope Collaboration, Astrophys. J. Lett. 875, L6 (2019)

  • [7]

    The Event Horizon Telescope Collaboration, et al., Astrophys. J. Lett. 930, L12 (2022)

  • [8]

    The Event Horizon Telescope Collaboration, et al., Astrophys. J. Lett. 930, L13 (2022)

  • [9]

    The Event Horizon Telescope Collaboration, et al., Astrophys. J. Lett. 930, L14 (2022)

  • [10]

    The Event Horizon Telescope Collaboration, et al., Astrophys. J. Lett. 930, L15 (2022)

  • [11]

    The Event Horizon Telescope Collaboration, et al., Astrophys. J. Lett. 930, L16 (2022)

  • [12]

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

  • [13]

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

  • [14]

    J. M. Bardeen, C. DeWitt, and B. DeWitt, Gordon and Breach, New York, (1973), p. 215-239

  • [15]

    J. P. Luminet, Astron. Astrophys. 75, 228 (1979)

  • [16]

    S. Chandrasekhar, (Oxford University Press, New York, 1992)

  • [17]

    K. Hioki and K. I. Maeda, Phys. Rev. D 80, 024042 (2009), arXiv: 0904.3575

  • [18]

    Z. Li and C. Bambi, J. Cosmol. Astropart. Phys. 1401, 041 (2014), arXiv: 1309.1606

  • [19]

    L. Yang and Z. Li, Int. J. Mod. Phys. D 25, 1650026 (2016), arXiv: 1511.00086v2

  • [20]

    S. Wei, Y. Liu, and R. B. Mann, Phys. Rev. D 99, 041303 (2019), arXiv: 1811.00047v3

  • [21]

    R. Kumar and S. G. Ghosh, Astrophys. J 892, 78 (2020), arXiv: 1811.01260v4

  • [22]

    Z. Chang, and Q. Zhu, J. Cosmol. Astropart. Phys. 09, 003 (2021), arXiv: 2104.14221v2

  • [23]

    S. Wei and Y. Zou, arXiv: 2108.02415v1

  • [24]

    X. Hou, Z. Xu, M. Zhou et al., J. Cosmol. Astropart. Phys. 07, 015 (2018)

  • [25]

    R. A. Konoplya, Phys. Lett. B 795, 1 (2019), arXiv: 1905.00064

  • [26]

    K. Jusufi, M. Jamil, P. Salucci et al., Phys. Rev. D 100, 044012 (2019)

  • [27]

    M. Jamil, K. Jusufi, K. Lin et al., Phys. Rev. D 99, 044015 (2019)

  • [28]

    K. Jusufi, M. Jamil, and T. Zhu, Eur. Phys. J. C 80, 354 (2020)

  • [29]

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

  • [30]

    S.a Dastan, R. Saffari, and S. Soroushfar, Eur. Phys. J. Plus 137, 1002 (2022), arXiv: 1606.06994

  • [31]

    R. Kumara, B. P. Singha, and S. G. Ghosh, Annals Phys. 420, 168252 (2020), arXiv: 1904.07652v2

  • [32]

    F. Long, S. B. Chen, M. Z. Wang et al., Eur. Phys. J. C 80, 1180 (2020)

  • [33]

    A. Stepanian, Sh. Khlghatyan, and V.G. Gurzadyan, Eur. Phys. J. Plus 136, 127 (2021)

  • [34]

    V. Prokopov, S. Alexeyev and O. Zenin, J. Exp. Theor. Phys. 135, 91 (2022), arXiv: 2107.01115

  • [35]

    Z. Younsi, D. Psaltis, and F. O¨O¨zel, Apj 942, 47 (2023), arXiv: 2111.01752

  • [36]

    J. L. Jing, S. Long, W. K. Deng et al., Phys. Mech. Astron. 65, 100411 (2022), arXiv: 2208.02420

  • [37]

    J. L. Jing, S. Chen, M. M Sun et al., Phys. Mech. Astron. 65, 260411 (2022), arXiv: 2112.09838

  • [38]

    J. L. Jing, W. K. Deng, S. Long et al., Phys. Mech. Astron. 66, 270411 (2023)

  • [39]

    Y. H. Zou, M. J. Wang, J. L Jing et al., Phys. Mech. Astron. 64, 250411 (2021)

  • [40]

    W. T. Liu, X. J Fang, J. L. Jing et al., Phys. Mech. Astron. 66, 210411 (2023)

  • [41]

    X. Zhou, S. B. Chen, J. L. Jing et al., Phys. Mech. Astron. 65, 250411 (2022)

  • [42]

    L. OuYang, D. Wang, X. Y. Qiao et al., Phys. Mech. Astron. 64, 240411 (2021)

  • [43]

    R. Shaikh, P. Kocherlakota, R. Narayan et al., MNRAS 482, 1 (2019)

  • [44]

    D. Dey, R. Shaikh, and P. S. Joshi, Phys. Rev. D 102, 124015 (2021)

  • [45]

    A. B. Joshi, D. Dey, P. S. Joshi et al., Phys. Rev. D 102, 024022 (2020)

  • [46]

    V. Patel, D. Tahelyani, A. B. Joshi et al., Eur. Phys. J. C 82, 798 (2022)

  • [47]

    S. Y. Wang, S. B. Chen, and J. L. Jing, J. Cosmol. Astropart. Phys. 11, 020 (2016), arXiv: 1609.00802v2

  • [48]

    M. Z. Wang, S. B. Chen, and J. L. Jing, J. Cosmol. Astropart. Phys. 10, 051 (2017)

  • [49]

    M. Z. Wang, S. B. Chen, and J. L. Jing, Phys. Rev. D 104, 084021 (2021), arXiv: 2104.12304v2

  • [50]

    M. Z. Wang, S. B. Chen, J. C. Wang et al., Eur. Phys. J. C 80, 110 (2020)

  • [51]

    M. Z. Wang, S. B. Chen, and J. L. Jing, Eur. Phys. J. C 81, 509 (2021), arXiv: 1908.04527

  • [52]

    M. Z. Wang, S. B. Chen, and J. L. Jing, Phys. Rev. D 97, 064029 (2018)

  • [53]

    M. Z. Wang, S. B. Chen, and J. L. Jing, Phys. Rev. D 98, 104040 (2018)

  • [54]

    M. Z. Wang, G. H. Guo, S. B. Chen et al., Chin. Phys. C 47, 015102 (2023), arXiv: 2112.04170

  • [55]

    S. B. Chen, M. Z. Wang, and J. L. Jing, JHEP 07, 054 (2020), arXiv: 2004.08857v3

  • [56]

    M. Z. Wang, S. B. Chen, and J. L. Jing, Commun. Theor. Phys. 74, 097401 (2022), arXiv: 2205.05855

  • [57]

    P. V. P. Cunha, C. A. R. Herdeiro, E. Radu et al., Phys. Rev. Lett. 115, 211102 (2015), arXiv: 1509.00021

  • [58]

    P. V. P. Cunha, C. A. R. Herdeiro, E. Radu et al., Int. J. Mod. Phys. D 25, 1641021 (2016), arXiv: 1605.08293

  • [59]

    F. H. Vincent, E. Gourgoulhon, C. A. R. Herdeiro et al., Phys. Rev. D 94, 084045 (2016), arXiv: 1606.04246

  • [60]

    P. V. P. Cunha, J. Grover, C. A. R. Herdeiro et al., Phys. Rev. D 94, 104023 (2016)

  • [61]

    T. Johannsen, Astrophys. J. 777, 170 (2013)

  • [62]

    M. Z. Wang, S. B. Chen, J. L. Jing et al., Phys. Mech. Astron. 66, 110411 (2023), arXiv: 2208.10219

  • [63]

    E. Teo, Gen. Rel. Grav. 53(1), 10 (2021)

  • [64]

    P. V. P. Cunha, C. A. R. Herdeiro, and E. Radu, Phys. Rev. D 96, 024039 (2017)

  • [65]

    V. Perlick, O. Y. Tsupko, and G. S. Bisnovatyi-Kogan, Phys. Rev. D 92, 104031 (2015)

  • [66]

    A. Grenzebach, V. Perlick, and C. Lammerzahl, Phys. Rev. D 89, 124004 (2014)

  • [67]

    P. V. P. Cunha1 and C. A. R. Herdeiro, Gen. Rel. Grav. 50, 42 (2018), arXiv: 1801.00860

  • [68]

    S. W. Wei, Y. C. Zou, Y. X. Liu et al., J. Cosmol. Astropart. Phys. 08, 030 (2019), arXiv: 1904.07710

  • [69]

    F. Long, J. C. Wang, S. B. Chen et al., JHEP 10, 269 (2019)

  • [70]

    X. X. Zeng and H. Q. Zhang, Eur. Phys. J. C 80, 1058 (2020)

  • [71]

    X. X. Zeng, H. Q. Zhang, and H. Zhang, Eur. Phys. J. C 80, 872 (2020)

  • [72]

    J. Grover and A. Wittig, Phys. Rev. D 96, 024045 (2017)

  • [73]

    X. Qin, S. B. Chen, and J. L. Jing, Class. Quantum Grav. 38, 115008 (2021), arXiv: 2011.04310

  • [74]

    Z. L. Zhang, S. B. Chen, X. Qin et al., Eur. Phys. J. C 81, 991 (2021), arXiv: 2106.07981

  • [75]

    X. Qin, S. B. Chen, and J. L. Jing, Eur. Phys. J. C 82, 784 (2022), arXiv: 2111.10138

  • [76]

    X. Y. Liu, S. B. Chen, J. L. Jing et al., Phys. Mech. Astron. 65, 120411 (2022), arXiv: 2205.00391

  • [77]

    Z. L. Zhang, S. B. Chen, and J. L. Jing, Eur. Phys. J. C 82, 835 (2022), arXiv: 2205.13696

  • [78]

    X. Qin, S. B. Chen, Z. L. Zhang et al., Astrophys. J. 938, 2 (2022), arXiv: 2207.12034

  • [79]

    S. B. Chen, J. L. Jing, W. L. Qian et al., Accepted by Sci. China, Phys. Mech. Astron. (2023), arXiv: 2301.00113

  • [80]

    X. Qin, S. B. Chen, Z. L. Zhang et al., Eur. Phys. J. C 83, 159 (2023), arXiv: 2301.01551

  • [81]

    R. Konoplya and A. Zhidenko, Phys. Lett. B 756, 350 (2016)

  • [82]

    E. Franzin, S. Liberati, and M. Oi, Phys. Rev. D 103, 104032 (2021)

  • [83]

    P. H. C. Siqueira and M. Richartz, Phys. Rev. D 106, 024046 (2022)

  • [84]

    N. Tsukamoto, T. Harada, and K. Yajima, Phys. Rev. D 86, 104062 (2012)