• [1]

    S. Refsdal, Mon. Not. Roy. Astron. Soc. 128, 307 (1964)

  • [2]

    K. S. Virbhadra and C. R. Keeton, Phys. Rev. D 77, 124014 (2008), arXiv:0710.2333[gr-qc

  • [3]

    E. F. Eiroa and C. M. Sendra, Phys. Rev. D 88(10), 103007 (2013), arXiv:1308.5959[gr-qc

  • [4]

    C. R. Keeton and L. A. Moustakas, Astrophys. J. 699, 1720 (2009), arXiv:0805.0309[astro-ph

  • [5]

    D. Coe and L. Moustakas, Astrophys. J. 706, 45 (2009), arXiv:0906.4108[astroph.CO

  • [6]

    E. V. Linder, Phys. Rev. D 84, 123529 (2011), arXiv:1109.2592[astroph.CO

  • [7]

    S. H. Suyu et al., Astrophys. J. 788, L35 (2014), arXiv:1306.4732[astroph.CO

  • [8]

    V. Bonvin et al., Mon. Not. Roy. Astron. Soc. 465(4), 4914 (2017), arXiv:1607.01790[astroph.CO

  • [9]

    T. Treu and P. J. Marshall, Astron. Astrophys. Rev. 24(1), 11 (2016), arXiv:1605.05333[astroph.CO

  • [10]

    K. Liao, X. L. Fan, X. H. Ding et al., Nature Commun. 8(1), 1148 (2017) Erratum: [Nature Commun. 8(1), 2136 (2017)] doi:10.1038/s41467-017-01152-9, 10.1038/s41467-017-02135-6, arXiv:1703.04151 [astro-ph.CO]

  • [11]

    K. Hirata et al. (Kamiokande-II Collaboration), Phys. Rev. Lett. 58, 1490 (1987)

  • [12]

    R. M. Bionta et al., Phys. Rev. Lett. 58, 1494 (1987)

  • [13]

    M. G. Aartsen et al. (IceCube and Fermi-LAT and MAGIC and AGILE and ASAS-SN and HAWC and H.E.S.S. and INTEGRAL and Kanata and Kiso and Kapteyn and Liverpool Telescope and Subaru and Swift NuSTAR and VERITAS and VLA/17B-403 Collaborations), Science 361, no. 6398, eaat1378 (2018)

  • [14]

    M. G. Aartsen et al. (IceCube Collaboration), Science 361(6398), 147 (2018)

  • [15]

    B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. Lett. 116(6), 061102 (2016), arXiv:1602.03837[gr-qc

  • [16]

    B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations]), Phys. Rev. Lett. 116(24), 241103 (2016), arXiv:1606.04855[gr-qc

  • [17]

    B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. Lett. 119(14), 141101 (2017), arXiv:1709.09660[gr-qc

  • [18]

    B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. Lett. 119(16), 161101 (2017), arXiv:1710.05832[gr-qc

  • [19]

    B. P. Abbott et al. (LIGO Scientific and Virgo and FermiGBM and INTEGRAL Collaborations), Astrophys. J. 848(2), L13 (2017), arXiv:1710.05834[astro-ph.HE

  • [20]

    P. L. Kelly et al., Science 347, 1123 (2015), arXiv:1411.6009[astro-ph.CO

  • [21]

    A. Goobar et al., Science 356, 291 (2017), arXiv:1611.00014[astro-ph.CO

  • [22]

    M. Tanabashi et al. (Particle Data Group), Phys. Rev. D 98(3), 030001 (2018)

  • [23]

    J. Sakstein and B. Jain, Phys. Rev. Lett. 119(25), 251303 (2017)

  • [24]

    T. Baker, E. Bellini, P. G. Ferreira et al., Phys. Rev. Lett. 119(25), 251301 (2017)

  • [25]

    X. L. Fan, K. Liao, M. Biesiada et al., Phys. Rev. Lett. 118(9), 091102 (2017)

  • [26]

    J. J. Wei and X. F. Wu, Mon. Not. Roy. Astron. Soc. 472(3), 2906 (2017), arXiv:1707.04152[astro-ph.CO

  • [27]

    T. Yang, B. Hu, R. G. Cai et al., Astrophys. J. 880, 50 (2019)

  • [28]

    J. Jia and H. Liu, Phys. Rev. D 100(12), 124050 (2019), arXiv:1906.11833[gr-qc

  • [29]

    J. Bardeen, Proceedings of GR5, eds. C. DeWitt and B. DeWitt, Gordon and Breach (1968), p. 174

  • [30]

    E. Ayon-Beato and A. Garcia, Phys. Lett. B 493, 149 (2000), arXiv:gr-qc/0009077

  • [31]

    A. I. Janis, E. T. Newman, and J. Winicour, Phys. Rev. Lett. 20, 878 (1968)

  • [32]

    N. Breton, Class. Quant. Grav. 19, 601 (2002)

  • [33]

    E. F. Eiroa, Phys. Rev. D 73, 043002 (2006), arXiv:gr-qc/0511065

  • [34]

    S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, John Wiley & Sons (1972)

  • [35]

    I. S. Gradshteyn, and I. M. Ryzhik, Table of Integrals, Series, and Products, 8th ed. Academic Press (2014), p. 152

  • [36]

    G. W. Richter and R. A. Matzner, Phys. Rev. D 28, 3007 (1983)

  • [37]

    K. Huang and J. Jia, JCAP 08, 016 (2020), arXiv:2003.08250[gr-qc

  • [38]

    K. Akiyama et al. (Event Horizon Telescope Collaboration]), Astrophys. J. 875(1), L1 (2019), arXiv:1906.11238[astro-ph.GA

  • [39]

    H. Liu and J. Jia, Eur. Phys. J. C 80(10), 932 (2020), arXiv:2006.11125[gr-qc