• [1]

    P. G. S. Fernandes, Phys. Rev. D 108(6), L061502 (2023), arXiv:2305.10382[gr-qc]

  • [2]

    D. M. Capper and M. J. Duff, Nuovo Cim. A 23, 173 (1974)

  • [3]

    S. Deser and A. Schwimmer, Phys. Lett. B 309, 279 (1993), arXiv:hep-th/9302047

  • [4]

    R.-G. Cai, L.-M. Cao, and N. Ohta, JHEP 04, 082 (2010), arXiv:0911.4379[hep-th]

  • [5]

    M. Guo and P.-C. Li, Eur. Phys. J. C 80(6), 588 (2020), arXiv:2003.02523[gr-qc]

  • [6]

    X.-X. Zeng, H.-Q. Zhang, and H. Zhang, Eur. Phys. J. C 80(9), 872 (2020), arXiv:2004.12074[gr-qc]

  • [7]

    S. U. Islam, R. Kumar, and S. G. Ghosh, JCAP 09, 030 (2020), arXiv:2004.01038[gr-qc]

  • [8]

    R. A. Konoplya and A. F. Zinhailo, Eur. Phys. J. C 80(11), 1049 (2020), arXiv:2003.01188[gr-qc]

  • [9]

    S. Tsujikawa, Phys. Lett. B 843, 138054 (2023), arXiv:2304.10019[gr-qc]

  • [10]

    J. Jiang and M. Zhang, arXiv: 2305.12345[gr-qc]

  • [11]

    M. Gurses and B. Tekin, Phys. Rev. D 109(2), 024001 (2024), arXiv:2310.00312[gr-qc]

  • [12]

    K. Akiyama et al. (Event Horizon Telescope Collaboration), Astrophys. J. Lett. 875, L1 (2019), arXiv:1906.11238[astro-ph.GA]

  • [13]

    K. Akiyama et al. (Event Horizon Telescope Collaboration), Astrophys. J. Lett. 930(2), L12 (2022)

  • [14]

    R.-S. Lu et al., Nature 616(7958), 686 (2023), arXiv:2304.13252[astro-ph.HE]

  • [15]

    S. Vagnozzi et al., Class. Quant. Grav. 40(16), 165007 (2023), arXiv:2205.07787[gr-qc]

  • [16]

    S. Chen, J. Jing, W.-L. Qian et al., Sci. China Phys. Mech. Astron. 66(6), 260401 (2023), arXiv:2301.00113[astro-ph.HE]

  • [17]

    P. V. P. Cunha, E. Berti, and C. A. R. Herdeiro, Phys. Rev. Lett. 119(25), 251102 (2017), arXiv:1708.04211[gr-qc]

  • [18]

    P. V. P. Cunha and C. A. R. Herdeiro, Phys. Rev. Lett. 124(18), 181101 (2020), arXiv:2003.06445[gr-qc]

  • [19]

    M. Guo and S. Gao, Phys. Rev. D 103(10), 104031 (2021), arXiv:2011.02211[gr-qc]

  • [20]

    R. Ghosh and S. Sarkar, Phys. Rev. D 104(4), 044019 (2021), arXiv:2107.07370[gr-qc]

  • [21]

    M. Heydari-Fard, M. Heydari-Fard, and H. R. Sepangi, Eur. Phys. J. C 81(5), 473 (2021), arXiv:2105.09192[gr-qc]

  • [22]

    J. Peng, M. Guo, and X.-H. Feng, Chin. Phys. C 45(8), 085103 (2021), arXiv:2008.00657[gr-qc]

  • [23]

    Z. Zhang, H. Yan, M. Guo et al., Phys. Rev. D 107(2), 024027 (2023), arXiv:2206.04430[gr-qc]

  • [24]

    Y. Meng, X.-M. Kuang, and Z.-Y. Tang, Phys. Rev. D 106(6), 064006 (2022), arXiv:2204.00897[gr-qc]

  • [25]

    A. He, J. Tao, P. Wang et al., Eur. Phys. J. C 82(8), 683 (2022), arXiv:2205.12779[gr-qc]

  • [26]

    P. V. P. Cunha, N. A. Eiró, C. A. R. Herdeiro et al., JCAP 03, 035 (2020), arXiv:1912.08833[gr-qc]

  • [27]

    Z. Zhang, S. Chen, X. Qin et al., Eur. Phys. J. C 81(11), 991 (2021), arXiv:2106.07981[gr-qc]

  • [28]

    Y. Hou, P. Liu, M. Guo et al., Class. Quant. Grav. 39(19), 194001 (2022), arXiv:2203.02755[gr-qc]

  • [29]

    Y. Hou, Z. Zhang, H. Yan et al., Phys. Rev. D 106(6), 064058 (2022), arXiv:2206.13744[gr-qc]

  • [30]

    X.-J. Wang, X.-M. Kuang, Y. Meng et al., Phys. Rev. D 107(12), 124052 (2023), arXiv:2304.10015[gr-qc]

  • [31]

    C. Zhang, Y. Ma, and J. Yang, Phys. Rev. D 108(10), 104004 (2023), arXiv:2302.02800[gr-qc]

  • [32]

    S. Hu, C. Deng, S. Guo et al., Eur. Phys. J. C 83(3), 264 (2023)

  • [33]

    A. E. Héloïse Delaporte and A. Held, Class. and Quant. Grav. 39(13), 134002 (2022), arXiv:2003.00105[gr-qc]

  • [34]

    T. Zi and P.-C. Li, arXiv: 2311.07279[gr-qc]

  • [35]

    R. Kumar and S. G. Ghosh, JCAP 07, 053 (2020), arXiv:2003.08927[gr-qc]

  • [36]

    S. E. Gralla, D. E. Holz, and R. M. Wald, Phys. Rev. D 100(2), 024018 (2019), arXiv:1906.00873[astro-ph.HE]

  • [37]

    Z. Hu, Z. Zhong, P.-C. Li et al., Phys. Rev. D 103(4), 044057 (2021), arXiv:2012.07022[gr-qc]

  • [38]

    S. E. Gralla, A. Lupsasca, and A. Strominger, Mon. Not. Roy. Astron. Soc. 475(3), 3829 (2018), arXiv:1710.11112[astro-ph.HE]

  • [39]

    J. M. Bardeen and G. T. Horowitz, Phys. Rev. D 60, 104030 (1999), arXiv:hep-th/9905099

  • [40]

    Y. Hou, Z. Zhang, M. Guo et al., Phys. Rev. D 107(12), 124014 (2023), arXiv:2301.08467[gr-qc]

  • [41]

    A. Chael, M. D. Johnson, and A. Lupsasca, Astrophys. J. 918(1), 6 (2021), arXiv:2106.00683[astro-ph.HE]

  • [42]

    A. Mummery and S. Balbus, Mon. Not. Roy. Astron. Soc. 521(2), 2439 (2023), arXiv:2302.14437[astro-ph.HE]