- [1]
C. M. Will, Living Rev. Relativ.9, 3 (2006)
- [2]
C. M. Will, Living Rev. Relativ.17, 4 (2014)
- [3]
P. Schneider, J. Ehlers, and E. E. Falco, Gravitational Lenses. 1992.
- [4]
M. Bartelmann, Class. Quantum Grav.27, 233001 (2010)
- [5]
K. Akiyama andet al. (Event Horizon Telescope Collaboration), Astrophys. J.910, L12 (2021)
- [6]
K. Akiyama andet al. (Event Horizon Telescope Collaboration), Astrophys. J.910, L13 (2021)
- [7]
K. Akiyama andet al. (Event Horizon Telescope Collaboration), Astrophys. J.875, L1 (2019)
- [8]
K. Akiyama andet al. (Event Horizon Telescope Collaboration), Astrophys. J.875, L3 (2019)
- [9]
C. Goddi, H. Falcke, M. Krameret al., Int. J. Mod. Phys. D26, 1730001 (2017)
- [10]
X. Jiang, X. Ren, Z. Liet al., Mon. Not. R. Astron. Soc.528, 1965 (2024)
- [11]
X.-M. Kuang, Z.-Y. Tang, B. Wanget al., Phys. Rev. D106, 064012 (2022)
- [12]
S.-S. Zhao and Y. Xie, European Physical Journal C77, 272 (2017)
- [13]
S. Chen and J. Jing, Class. Quantum Grav.27, 225006 (2010)
- [14]
T. L. Smith, arXiv: 0907.4829
- [15]
A. Ditta, X. Tiecheng, F. Atamurotovet al., Chin. J. Phys.83, 664 (2023)
- [16]
R. C. Pantig, L. Mastrototaro, G. Lambiaseet al., Eur. Phys. J. C82(12), 1155 (2022)
- [17]
S. I. Kruglov, Int. J. Mod. Phys. D31(04), 2250025 (2022)
- [18]
Z. Turakhonov, F. Atamurotov, A. Ovgunet al., Commun. Theor. Phys.76(11), 115401 (2024)
- [19]
B. Rahmatov, M. Zahid, S. U. Khanet al., Chin. Phys. C49(7), 075105 (2025)
- [20]
A. Al-Badawi, Y. Sekhmani, and K. Boshkayev, Phys. Dark Univ.48, 101865 (2025)
- [21]
H. P. Saikia, M. M. Gohain, and K. Bhuyan, arXiv: 2504.13466
- [22]
D. Flores-Alfonso, B. A. González-Morales, R. Linareset al., Phys. Lett. B812, 136011 (2021)
- [23]
K. Karshiboev, F. Atamurotov, A. Övgünet al., New Astron.109, 102200 (2024)
- [24]
B. Eslam Panah, PTEP2024(2), 023E01 (2024)
- [25]
H. Kim, Phys. Rev. D61, 085014 (2000)
- [26]
M. Born and L. Infeld, Proc. Roy. Soc. Lond. A144(852), 425 (1934)
- [27]
G. W. Gibbons, AIP Conf. Proc.589(1), 324 (2001)
- [28]
I. Bandos, K. Lechner, D. Sorokinet al., Phys. Rev. D102, 121703 (2020)
- [29]
V. Perlick, Living Rev. Relativ.7, 9 (2004)
- [30]
G. W. Gibbons and C. A. R. Herdeiro, Class. Quant. Grav.18, 1677 (2001)
- [31]
R. Ruffini, Y.-B. Wu, and S.-S. Xue, Phys. Rev. D88, 085004 (2013)
- [32]
B. P. Kosyakov, Phys. Lett. B810, 135840 (2020)
- [33]
T. Clifton, P. G. Ferreira, A. Padillaet al., Phys. Rep.513, 001 (2012)
- [34]
C. G. Böhmer and E. Jensko, Phys. Rev. D104, 024010 (2021)
- [35]
S. Nojiri and S. D. Odintsov, Phys. Rep505, 59 (2011)
- [36]
T. P. Sotiriou and S.-Y. Zhou, Phys. Rev. Lett.112, 251102 (2014)
- [37]
S. Capozziello and M. de Laurentis, Phys. Rep.509, 167 (2011)
- [38]
E. Berti andet al., Class. Quantum Grav.32, 243001 (2015)
- [39]
A. De Felice and S. Tsujikawa, Living Rev. Relativ.13, 3 (2010)
- [40]
K. Koyama, Reports on Progress in Physics79, 046902 (2016)
- [41]
L. Heisenberg, Phys. Rep.796, 001 (2019)
- [42]
J. Rayimbaev, R. C. Pantig, A. Övgünet al., Annals of Physics454, 169335 (2023)
- [43]
B. Puliçe, R. C. Pantig, A. Övgünet al., Class. Quantum Grav.40, 195003 (2023)
- [44]
S. Vagnozzi, R. Roy, Y.-D. Tsaiet al., Class. Quantum Grav.40, 165007 (2023)
- [45]
A. Uniyal, R. C. Pantig, and A. Övgün, Physics of the Dark Universe40, 101178 (2023)
- [46]
R. C. Pantig and A. Övgün, Annals of Physics448, 169197 (2023)
- [47]
F. Atamurotov, U. Papnoi, and K. Jusufi, Class. Quantum Grav.39, 025014 (2022)
- [48]
E. Ghorani, B. Puliçe, F. Atamurotovet al., Eur. Phys. J. C83, 318 (2023)
- [49]
H. Hoshimov, O. Yunusov, F. Atamurotovet al., Physics of the Dark Universe43, 101392 (2024)
- [50]
R. Kumar, S. U. Islam, and S. G. Ghosh, European Physical Journal C80, 1128 (2020)
- [51]
S. U. Islam, R. Kumara, and S. G. Ghosha, J. Cosmol. A. P2020, 030 (2020)
- [52]
D. Psaltis, Living Rev. Relativ.11, 9 (2008)
- [53]
E. Berti, V. Cardoso, and A. O. Starinets, Class. Quantum Grav.26, 163001 (2009)
- [54]
D. Psaltis andet al., Phys. Rev. Lett.125, 141104 (2020)
- [55]
N. K. Johnson-McDaniel, arXiv: 1905.05565
- [56]
S. W. Hawking and G. F. R. Ellis,The large-scale structure of space-time(Cambridge: Cambridge University Press, 1973)
- [57]
K. S. Thorne,Black holes and time warps: Einstein’s outrageous legacy(New York: W. W. Norton & Company, 1994).
- [58]
M. Volonteri, M. Habouzit, and M. Colpi, Nature Reviews Physics3, 732 (2021)
- [59]
R. Tsuda, R. Suzuki, and S. Tomizawa, arXiv: 2308.02146
- [60]
J. Barrientos, A. Cisterna, M. Hassaineet al., Phys. Lett. B860, 139214 (2025)
- [61]
B. Eslam Panah, A. Rincon, and N. Heidari, arXiv: 2411.02907
- [62]
J. F. Plebański and S. Hacyan, Journal of Mathematical Physics20, 1004 (1979)
- [63]
V. Bozza, Phys. Rev. D66, 103001 (2002)
- [64]
K. S. Virbhadra and G. F. R. Ellis, Phys. Rev. D62, 084003 (2000)
- [65]
K. S. Virbhadra, Phys. Rev. D79, 083004 (2009)
- [66]
K. Akiyama andet al., ApJL875, 44 (2019)
- [67]
V. Bozza and L. Mancini, General Relativity and Gravitation36, 435 (2004)