• [1]

    P. Rastall, Phys. Rev. D 6, 3357 (1972)

  • [2]

    A. M. Oliveira, H.E.S. Velten, J. C. Fabris et al., Phys.Rev.D 92, 044020 (2015)

  • [3]

    Y. Heydarzade and F. Darabi, Phys.Lett.B 771, 365 (2017)

  • [4]

    H. Moradpour, N. Sadeghnezhad, and S. H. Hendi, Can.J. Phys. 95, 1257 (2017)

  • [5]

    R. Kumar and S. Ghosh, Eur. Phys. J. C 78, 750 (2018)

  • [6]

    M. Visser, Phys. Lett. B 782, 83 (2018)

  • [7]

    F. Darabi, H. Moradpour, I. Licata et al, Eur. Phys. J. C 78, 25 (2018)

  • [8]

    G. Abbas and M. R. Shahzad, Eur. Phys. J. A 54, 211 (2018)

  • [9]

    D. Das, S. Dutta, and S. Chakraborty, Eur. Phys. J. C 78, 810 (2018)

  • [10]

    S. Hansraj, A. Banerjee, and P. Channuie, Annals Phys. 400, 320 (2019)

  • [11]

    X. C. Cai and Y. G. Miao, Phys. Rev. D 101, 104023 (2020)

  • [12]

    Z. Li and T. Zhou, Phys. Rev. D 104, 104044 (2021)

  • [13]

    K. Akiyama et al, Astrophys. J. L 1, 875 (2019)

  • [14]

    K. Akiyama et al, Astrophys. J. Lett. L 12, 930 (2022)

  • [15]

    N. I. Shakura and R. A. Sunyaev, Astron. Astrophys 24, 337 (1973)

  • [16]

    J. -P. Luminet, Astron. Astrophys. 75 , 1 (1979)

  • [17]

    A. Laor, Astrophys. J 376, 90 (1991)

  • [18]

    G. Gyulchev, P. Nedkova, T. Vetsov et al., Phys. Rev. D 100, 024055 (2019)

  • [19]

    S. Paul, R. Shaikh, P. Banerjee et al., JCAP 03, 055 (2020)

  • [20]

    F. Rahaman, T. Manna, R. Shaikh et al., Nucl. Phys. B 972, 115548 (2021)

  • [21]

    C. Q. Liu, L. Tang, and J. L. Jing, Int. J. Mod. Phys. D 31, 2250041 (2022)

  • [22]

    K. Meng and X. L. Fan, Dynamics of null particles and shadow for general rotating black hole, arXiv: 2307.08953.

  • [23]

    S. Guo, K. J. He, G. R. L et al, Class.Quant.Grav. 38, 165013 (2021)

  • [24]

    S. Guo, G. R. Li, and E. W. Liang, Class. Quant. Grav. 39, 135004 (2022)

  • [25]

    F. Rahaman, Peter K. F. Kuhfittig, K. Chakraborty et al, Int. J. Theor. Phys. 50, 2655 (2011)

  • [26]

    F. Rahaman, K. K. Nandi, A. Bhadra et al, Phys. Lett. B. 694, 10 (2011)

  • [27]

    V.V. Kiselev, Class. Quant. Grav. 20, 1187 (2003)

  • [28]

    A. Vikman, Phys. Rev. D. 71, 023515 (2005)

  • [29]

    I. D. Novikov, K. S. Thorne, in Black Holes, ed. C. DeWitt and B. DeWitt, (New York: Gordon and Breach 1973)

  • [30]

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

  • [31]

    R. Li, J. Wang, Z. Xu et al, Mon. Not. Roy. Astron. Soc. 486, 2407 (2019)

  • [32]

    L.V.E. Koopmans and T. Treu, Astrophys. J. 583, 606 (2003)