• [1]

    J. M. Bardeen, B. Carter, and S. W. Hawking, Commun. Math. Phys. 31, 161 (1973)

  • [2]

    P. J. Young, Phys. Rev. D 14, 3281 (1976)

  • [3]

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

  • [4]

    J. D. Bekenstein, Phys. Rev. D 51, R6608 (1995)

  • [5]

    S. W. Hawking, Commun. Math. Phys. 25, 167 (1972)

  • [6]

    T. P. Sotiriou and V. Faraoni, Phys. Rev. Lett. 108, 081103 (2012), arXiv:1109.6324[gr-qc

  • [7]

    L. Hui and A. Nicolis, Phys. Rev. Lett. 110, 241104 (2013), arXiv:1202.1296[hep-th

  • [8]

    B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. Lett. 116, 061102 (2016), arXiv:1602.03837[gr-qc

  • [9]

    K. Akiyama et al. (Event Horizon Telescope Collaboration), Astrophys. J. Lett. 875, L4 (2019), arXiv:1906.11241[astro-ph.GA

  • [10]

    J. P. Luminet, arXiv: 1902.11196[astro-ph.HE]

  • [11]

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

  • [12]

    A. De Felice and S. Tsujikawa, Living Rev. Rel. 13, 3 (2010), arXiv:1002.4928[gr-qc

  • [13]

    S. Nojiri and S. D. Odintsov, Phys. Rept. 505, 59 (2011), arXiv:1011.0544[gr-qc

  • [14]

    O. Aharony, S. S. Gubser, J. M. Maldacena et al., Phys. Rept. 323, 183 (2000), arXiv:hep-th/9905111[hep-th

  • [15]

    A. M. Awad and C. V. Johnson, Phys. Rev. D 62, 125010 (2000), arXiv:hep-th/0006037[hep-th

  • [16]

    E. Babichev, C. Charmousis, A. Lehébel et al., JCAP 09, 011 (2016), arXiv:1605.07438[gr-qc

  • [17]

    C. Erices and C. Martinez, Phys. Rev. D 97, 024034 (2018), arXiv:1707.03483[hep-th

  • [18]

    A. M. Awad, S. Capozziello, and G. G. L. Nashed, JHEP 07, 136 (2017), arXiv:1706.01773[gr-qc

  • [19]

    G. G. L. Nashed and E. N. Saridakis, Phys. Rev. D 102, 124072 (2020), arXiv:2010.10422[gr-qc

  • [20]

    T. P. Sotiriou and S. Y. Zhou, Phys. Rev. Lett. 112, 251102 (2014), arXiv:1312.3622[gr-qc

  • [21]

    H. O. Silva, J. Sakstein, L. Gualtieri et al., Phys. Rev. Lett. 120, 131104 (2018), arXiv:1711.02080[gr-qc

  • [22]

    D. D. Doneva and S. S. Yazadjiev, Phys. Rev. Lett. 120, 131103 (2018), arXiv:1711.01187[gr-qc

  • [23]

    G. Antoniou, A. Bakopoulos, and P. Kanti, Phys. Rev. Lett. 120, 131102 (2018), arXiv:1711.03390[hep-th

  • [24]

    C. A. R. Herdeiro, E. Radu, N. Sanchis-Gual et al., Phys. Rev. Lett. 121, 101102 (2018), arXiv:1806.05190[gr-qc

  • [25]

    P. G. S. Fernandes, C. A. R. Herdeiro, A. M. Pombo et al., Class. Quant. Grav. 36, 134002 (2019), [Erratum: Class. Quant. Grav. 37, 049501 (2020)], arXiv: 1902.05079[gr-qc]

  • [26]

    C. Y. Zhang, P. Liu, Y. Liu et al., Phys. Rev. D 104, 084089 (2021), arXiv:2103.13599[gr-qc

  • [27]

    D. C. Zou and Y. S. Myung, Phys. Rev. D 100, 124055 (2019), arXiv:1909.11859[gr-qc

  • [28]

    Y. S. Myung and D. C. Zou, Phys. Lett. B 811, 135905 (2020), arXiv:2009.05193[gr-qc

  • [29]

    P. Cunha, V. P., C. A. R. Herdeiro et al., Phys. Rev. D 96, 024039 (2017), arXiv:1705.05461[gr-qc

  • [30]

    P. V. P. Cunha and C. A. R. Herdeiro, Gen. Rel. Grav. 50, 42 (2018), arXiv:1801.00860[gr-qc

  • [31]

    W. L. Qian, S. Chen, C. G. Shao et al., Eur. Phys. J. C 82, 91 (2022), arXiv:2102.03820[gr-qc

  • [32]

    Y. Hou, M. Guo, and B. Chen, Phys. Rev. D 104, 024001 (2021), arXiv:2103.04369[gr-qc

  • [33]

    C. Bamber, S. J. Boege, T. Koffas et al., Phys. Rev. D 60, 092004 (1999)

  • [34]

    D. Tommasini, A. Ferrando, H. Michinel et al., Phys. Rev. A 77, 042101 (2008), arXiv:0802.0101[physics.optics

  • [35]

    P. Gaete and J. Helayël-Neto, Eur. Phys. J. C 74, 3182 (2014), arXiv:1408.3363[hep-th

  • [36]

    M. Novello, V. A. De Lorenci, J. M. Salim et al., Phys. Rev. D 61, 045001 (2000), arXiv:gr-qc/9911085[gr-qc

  • [37]

    C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation, (New York, NY:W. H. Freeman and Company, 1973)

  • [38]

    H. Yang, D. A. Nichols, F. Zhang et al., Phys. Rev. D 86, 104006 (2012), arXiv:1207.4253[gr-qc

  • [39]

    W. L. Qian, K. Lin, X. M. Kuang et al., Eur. Phys. J. C 82, 188 (2022), arXiv:2109.02844[gr-qc

  • [40]

    J. P. S. Lemos, Phys. Lett. B 353, 46 (1995), arXiv:gr-qc/9404041[gr-qc

  • [41]

    A. M. Awad, Class. Quant. Grav. 20, 2827 (2003), arXiv:hep-th/0209238[hep-th

  • [42]

    M. Wang, S. Chen, and J. Jing, Phys. Rev. D 97, 064029 (2018), arXiv:1710.07172[gr-qc

  • [43]

    F. H. Vincent, T. Paumard, E. Gourgoulhon et al., Class. Quant. Grav. 28, 225011 (2011), arXiv:1109.4769[gr-qc

  • [44]

    J. Shipley and S. R. Dolan, Class. Quant. Grav. 33, 175001 (2016), arXiv:1603.04469[gr-qc

  • [45]

    A. Bohn, W. Throwe, F. Hébert et al., Class. Quant. Grav. 32, 065002 (2015), arXiv:1410.7775[gr-qc

  • [46]

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

  • [47]

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

  • [48]

    F. H. Vincent, E. Gourgoulhon, C. Herdeiro et al., Phys. Rev. D 94, 084045 (2016), arXiv:1606.04246[gr-qc

  • [49]

    P. V. P. Cunha, J. Grover, C. Herdeiro et al., Phys. Rev. D 94, 104023 (2016), arXiv:1609.01340[gr-qc

  • [50]

    I. Banerjee, S. Chakraborty, and S. SenGupta, Phys. Rev. D 101, 041301 (2020), arXiv:1909.09385[gr-qc

  • [51]

    A. Chowdhuri and A. Bhattacharyya, Phys. Rev. D 104, 064039 (2021), arXiv:2012.12914[gr-qc