Strongly lensed gravitational waves as probes to test the cosmic distance duality relation

[1]
I. M. H. Etherington, Philosophical Magazine 15, 761 (1933)
[2]
I. M. H. Etherington, General Relativity and Gravitation 39, 1055 (2007)
[3]
G. F. R. Ellis, General Relativity and Cosmology, Enrico Fermi Summer School Course XLVⅡ, ed R. K. Sachs, 1971 (New York: Academic)
[4]
G. F. R. Ellis, Gen. Rel. Grav. 39, 1047 (2007)
[5]
P. S. Corasaniti, Mon. Not. Roy. Astron. Soc. 372, 191 (2006)
[6]
B. A. Bassett and M. Kunz, Phys. Rev. D 69, 101305 (2004)
[7]
G. F. R. Ellis, R. Poltis, J. P. Uzan et al., Phys. Rev. D 87, 103530 (2013)
[8]
Z. Li, P. Wu, and H. Yu, Astrophys. J 729, L14 (2011)
[9]
R. F. L. Holanda, J. A. S. Lima, and M. B. Ribeiro, Astrophys. J 722, L233 (2010)
[10]
R. F. L. Holanda, V. C. Busti, and J. S. Alcaniz, JCAP 1602, 054 (2016)
[11]
R. F. L. Holanda, V. C. Busti, F. S. Lima et al., JCAP 1709, 039 (2017)
[12]
N. Liang, Z. Li, P. Wu et al., MNRAS 436, 1017 (2013)
[13]
J. Hu and F. Y. Wang, Mon. Not. Roy. Astron. Soc. 477, 5064 (2018)
[14]
X. Li and H.-N. Lin, Mon. Not. Roy. Astron. Soc. 474, 313 (2018)
[15]
H.-N. Lin, M.-H. Li, and X. Li, Mon. Not. Roy. Astron. Soc. 480, 3117 (2018)
[16]
K. Liao, Astrophys. J. 885, 70 (2019)
[17]
K. Liao, Z. Li, S. Cao et al., Astrophys. J. 822, 74 (2016)
[18]
C. Ma and P. S. Corasaniti, Astrophys. J. 861, 124 (2018)
[19]
A. Piorkowska et al., Acta Physica Polonica B 42, 2297 (2011)
[20]
S. Santos-da-Costa, V. C. Busti, and R. F. L. Holanda, JCAP 1510, 061 (2015)
[21]
X. Yang, H. R. Yu, Z. S. Zhang et al., Astrophys. J. Lett 777, L24 (2013)
[22]
D. M. Scolnic et al., Astrophys. J. 859, 101 (2018)
[23]
B. P. Abbott et al., LIGO Scientific Collaboration and Virgo Collaboration, Phys. Rev. Lett. 116, 061102 (2016)
[24]
B. P. Abbott et al., LIGO Scientific Collaboration and Virgo Collaboration. Astrophys, J. Lett. 848, L13 (2017)
[25]
T. Delubac et al., A&A 574, A59 (2015)
[26]
M. Bonamente, M. K. Joy, S. J. LaRoque et al., Astrophys. J. 647, 25 (2006)
[27]
E. De Filippis, M. Sereno, M. W. Bautz et al., Astrophys. J. 625, 108 (2005)
[28]
J. C. Jackson and A. L. Jannetta, JCAP 0611, 002 (2006)
[29]
H.-N. Lin and X. Li, Chinese Physics C 44, 075101 (2020)
[30]
M. Biesiada, X. Ding, A. Piorkowska et al., JCAP 1410, 080 (2014)
[31]
X. Ding, M. Biesiada, and Z. H. Zhu, JCAP 1512, 006 (2015)
[32]
S. Mollerach and E. Roulet, Gravitational lensing and microlensing, (World Scientific, Singapore, 2002)
[33]
Einstein gravitational wave Telescope conceptual design study, http://www.et-gw.eu/et/
[34]
W. Zhao, C. Van Den Broeck, D. Baskaran et al., Phys. Rev. D 83, 023005 (2011)
[35]
B. S. Sathyaprakash and B. Schutz, Living Rev. Relativ. 12, 2 (2009)
[36]
A. Krolak and B. F. Schutz, Gen. Relativ. Gravit. 19, 1163 (1987)
[37]
C. K. Mishra, K. G. Arun, B. R. Iyer et al., Phys. Rev. D 82, 064010 (2010)
[38]
R. G. Cai, T. B. Liu, X. W. Liu et al., Phys. Rev. D 97, 103005 (2018)
[39]
B. S. Sathyaprakash, B. F. Schutz, and C. Van Den Broeck, Class. Quant. Grav. 27, 215006 (2010)
[40]
R. G. Cai and T. Yang, Phys. Rev. D 95, 044024 (2017)
[41]
Y. Wang, A. Stebbins, and E. L. Turner, Phys. Rev. Lett. 77, 2875 (1996)
[42]
B. Zhang, Astrophys. J. Lett 827, L31 (2016)
[43]
F. Fraschetti, JCAP 04, 054 (2018)
[44]
R. Perna, D. Lazzati, and B. Giacomazzo, Astrophys. J. Lett 821, L18 (2016)
[45]
Y.-Y. Choi, C. Park, and M.S. Vogeley, Astrophys. J. 658, 884 (2007)
[46]
S. Cao, M. Biesiada, R. Gavazzi et al., Astrophys. J. 806, 185 (2015)
[47]
S. Cao, J. Qi, Z. Cao et al., Sci. Rep. 9, 11608 (2019)
[48]
K. Liao, X. L. Fan, X. H. Ding et al., Nature Commun. 8, 1148 (2017); [Erratum: Nature Commun. 8, 2136 (2017)]
[49]
W. Zhao and L. Wen, Phys. Rev. D 97, 064031 (2018)
[50]
H. Y. Chen, M. Fishbach, and D. E. Holz, Nature 562, 545 (2018)
[51]
S. Mukherjee, B. D. Wandelt, S. M. Nissanke et al., arXiv: 2007.02943 [astro-ph.CO]