- [1]
A. S. Eddington,Space, time and gravitation. an outline of the general relativity theory(1920)
- [2]
F. W. Dyson, A. S. Eddington, and C. Davidson, Phil. Trans. R. Soc.220, 291 (1920)
- [3]
V. Perlick, Living Rev. Relativ.7, 9 (2004)
- [4]
K. S. Virbhadra, Phys. Rev. D79, 083004 (2009), arXiv: 0810.2109[gr-qc]
- [5]
K. S. Virbhadra and C. R. Keeton, Phys. Rev. D77, 124014 (2008), arXiv: 0710.2333[gr-qc]
- [6]
K. S. Virbhadra and G. F. Ellis, Phys. Rev. D65, 103004 (2002)
- [7]
K. S. Virbhadra, D. Narasimha, and S. M. Chitre, Astronomy and Astrophysics337, 1 (1998), arXiv: 9801174[astro-ph]
- [8]
C. M. Will, Class. Quant. Grav.32, 124001 (2015), arXiv: 1409.7812[physics.hist-ph]
- [9]
R. A. Vanderveld, M. J. Mortonson, W. Huet al., Phys. Rev. D85, 103518 (2012), arXiv: 1203.3195[astro-ph.CO]
- [10]
H. J. He and Z. Zhang, J. Cosmol. A. P.2017, 036 (2017), arXiv: 1701.03418
- [11]
S. Jung and C. S. Shin, Phys. Rev. Lett122, 041103 (2019), arXiv: 1712.01396[astro-ph.CO]
- [12]
P. Schneider, J. Ehlers, and E. E. Falco,Gravitational Lenses(1992)
- [13]
R. D. Blandford and R. Narayan, Annual Rev. Astron. Astrophys.30, 311 (1992)
- [14]
A. O. Petters, H. Levine, and J. Wambsganss,Singularity theory and gravitational lensing(2001)
- [15]
C. R. Keeton and A. O. Petters, Phys. Rev. D72, 104006 (2005), arXiv: gr-qc/0511019[gr-qc]
- [16]
M. C. Werner and A. O. Petters, Phys. Rev. D76, 064024 (2007), arXiv: 0706.0132[gr-qc]
- [17]
K. S. Virbhadra and G. F. R. Ellis, Phys. Rev. D.62, 084003 (2000)
- [18]
M. Sereno and F. de Luca, Phys. Rev. D74, 123009 (2006), arXiv: 0609435[astro-ph]
- [19]
V. Bozza, S. Capozziello, G. Iovaneet al., Gen. Rel. Grav.33, 1535 (2001), arXiv: 0102068[gr-qc]
- [20]
V. Bozza, Phys. Rev. D66, 103001 (2002), arXiv: 0208075[gr-qc]
- [21]
N. U. Molla, H. Chaudhary, G. Mustafaet al., Eur. Phys. J. C84, 574 (2024), arXiv: 2310.14234[gr-qc]
- [22]
S. E. Vázquez and E. P. Esteban, Nuovo Cim. B119, 489 (2004), arXiv: gr-qc/0308023
- [23]
S. U. Islam, J. Kumar, and S. G. Ghosh, J. Cosmol. A. P.2021, 013 (2021), arXiv: 2104.00696[gr-qc]
- [24]
J. Kumar, S. U. Islam, and S. G. Ghosh, Eur. Phys. J. C82, 443 (2022), arXiv: 2109.04450[gr-qc]
- [25]
N. U. Molla, S. G. Ghosh, and U. Debnath, Phys. Dark Universe44, 101495 (2024)
- [26]
S. S. Zhao and Y. Xie, Phys. Lett. B774, 357 (2017)
- [27]
M. Sereno, Mon. Not. Roy. Astron. Soc.344, 942 (2003), arXiv: astro-ph/0307243[astro-ph]
- [28]
A. S. Majumdar and N. Mukherjee, Mod. Phys. Lett. A20, 2487 (2005), arXiv: astro-ph/0403405[astro-ph]
- [29]
A. Övgün, K. Jusufi, and İ. Sakallı, Annals of Physics399, 193 (2018), arXiv: 1805.09431[gr-qc]
- [30]
R. C. Pantig and E. T. Rodulfo, Chin. J. Phys.66, 691 (2020), arXiv: 2003.00764[gr-qc]
- [31]
G. Mustafa, F. Atamurotov, I. Hussainet al., Chin. Phys. C46, 125107 (2022), arXiv: 2207.07608[gr-qc]
- [32]
H. Liu, J. Liang, and J. Jia, Class. Quant. Grav.39, 195013 (2022), arXiv: 2204.04519[gr-qc]
- [33]
A. Övgün, Phys. Rev. D99, 104075 (2019), arXiv: 1902.04411[gr-qc]
- [34]
W. Javed, M. B. Khadim, J. Abbaset al., Eur. Phys. J. Plus135, 314 (2020), arXiv: 2004.00408[gr-qc]
- [35]
C. Y. Wang, Y. F. Shen, and Y. Xie, J. Cosmol. A. P.2019, 022 (2019), arXiv: 1902.03789[gr-qc]
- [36]
G. N. Gyulchev and S. S. Yazadjiev, Phys. Rev. D81, 023005 (2010), arXiv: 0909.3014[gr-qc]
- [37]
K. Jusufi, A. Övgün, J. Saavedraet al., Phys. Rev. D97, 124024 (2018), arXiv: 1804.00643[gr-qc]
- [38]
N. Parbin, D. J. Gogoi, and U. D. Goswami, Phys. Dark Universe41, 101265 (2023), arXiv: 2305.09157[gr-qc]
- [39]
V. Perlick,Ray Optics, Fermat's Principle, and Applications to General Relativity, Vol. 61 (2000)
- [40]
O. Y. Tsupko and G. S. Bisnovatyi-Kogan, Gravitation and Cosmology15, 184 (2009)
- [41]
G. S. Bisnovatyi-Kogan and O. Y. Tsupko, Mon. Not. R. Astron. Soc.404, 1790 (2010)
- [42]
A. Rogers, Mon. Not. Roy. Astron. Soc.451, 17 (2015), arXiv: 1505.06790[gr-qc]
- [43]
X. Er and A. Rogers, Mon. Not. R. Astron. Soc.475, 867 (2018), arXiv: 1712.06900[astro-ph.GA]
- [44]
F. Atamurotov, S. Shaymatov, P. Sheoranet al., J. Cosmol. A. P.2021, 045 (2021), arXiv: 2105.02214[gr-qc]
- [45]
G. Z. Babar, F. Atamurotov, and A. Z. Babar, Phys. Dark Universe32, 100798 (2021)
- [46]
G. Z. Babar, F. Atamurotov, S. Ul Islamet al., Rev. D103, 084057 (2021), arXiv: 2104.00714[gr-qc]
- [47]
A. Hakimov and F. Atamurotov, Astrophys. Space. Sci.361, 112 (2016)
- [48]
F. Atamurotov, A. Abdujabbarov, and J. Rayimbaev, Eur. Phys. J. C81, 118 (2021)
- [49]
C. Benavides-Gallego, A. Abdujabbarov, and Bambi, Eur. Phys. J. C.78, 694 (2018)
- [50]
O. Y. Tsupko, Phys. Rev D103, 104019 (2021), arXiv: 2102.00553[gr-qc]
- [51]
W. Javed, I. Hussain, and A. Övgün, Eur. Phys. J. Plus137, 148 (2022), arXiv: 2201.09879[gr-qc]
- [52]
G. Crisnejo and E. Gallo, Phys. Rev. D97, 124016 (2018), arXiv: 1804.05473[gr-qc]
- [53]
H. Chakrabarty, A. B. Abdikamalov, A. A. Abdujabbarovet al., Phys. Rev. D.98, 024022 (2018)
- [54]
H. Hoshimov, O. Yunusov, F. Atamurotovet al., Phys. Dark Universe43, 101392 (2024), arXiv: 2312.10678[gr-qc]
- [55]
F. Atamurotov, O. Yunusov, A. Abdujabbarovet al., New Astronomy105, 102098 (2024)
- [56]
F. Atamurotov, H. Alibekov, A. Abdujabbarovet al., Symmetry15, 848 (2023)
- [57]
F. Atamurotov, I. Hussain, G. Mustafaet al., Chin. Phys. C47, 025102 (2023)
- [58]
F. Atamurotov and S. G. Ghosh, Eur. Phys. J. Plus137, 662 (2022)
- [59]
F. Atamurotov, F. Sarikulov, V. Khamidovet al., Eur. Phys. J. Plus137, 567 (2022)
- [60]
V. Perlick and O. Y. Tsupko, Phys. Rev. D.95, 104003 (2017), arXiv: 1702.08768[gr-qc]
- [61]
J. Badía and E. F. Eiroa, Phys. Rev. D104, 084055 (2021), arXiv: 2106.07601[gr-qc]
- [62]
F. Atamurotov, B. Ahmedov, and A. Abdujabbarov, Phys. Rev. D92, 084005 (2015), arXiv: 1507.08131[gr-qc]
- [63]
Q. Li, Y. Zhu, and T. Wang, Eur. Phys. J. C82, 2 (2022), arXiv: 2102.00957[gr-qc]
- [64]
A. Chowdhuri and A. Bhattacharyya, Phys. Rev. D104, 064039 (2021), arXiv: 2012.12914[gr-qc]
- [65]
Y. Pahlavon, F. Atamurotov, K. Jusufiet al., Phys. Dark Universe45, 101543 (2024), arXiv: 2406.09431[gr-qc]
- [66]
F. Atamurotov, M. Jamil, and K. Jusufi, Chin. Phys. C47, 035106 (2023), arXiv: 2212.12949[gr-qc]
- [67]
F. Atamurotov, I. Hussain, G. Mustafaet al., Eur. Phys. J. C82, 831 (2022), arXiv: 2209.01652[gr-qc]
- [68]
F. Tello-Ortiz, M. Ali Raza, M. Zubairet al., Phys. Dark Univ.44, 101460 (2024)
- [69]
M. Zubair, M. A. Raza, F. Sarikulovet al., JCAP10, 058 (2023), arXiv: 2305.16888[gr-qc]
- [70]
K. Akiyama andet al. (Event Horizon Telescope Collaboration), Astrophys. J.875, L1 (2019), arXiv: 1906.11238[astro-ph.GA]
- [71]
K. Akiyama andet al. (Event Horizon Telescope Collaboration), Astrophys. J.930, L12 (2022)
- [72]
K. Akiyama andet al. (Event Horizon Telescope Collaboration), Astrophys. J.930, L14 (2022)
- [73]
K. Akiyama andet al. (Event Horizon Telescope Collaboration), Astronomy and Astrophysics681, A79 (2024)
- [74]
A. Sen, Phys. Rev. Lett.69, 1006 (1992), arXiv: hep-th/9204046
- [75]
M. Guo, S. Song, and H. Yan, Phys. Rev. D101, 024055 (2020), arXiv: 1911.04796[gr-qc]
- [76]
S. G. Ghosh, R. Kumar, and S. U. Islam, J. Cosmol. A. P.2021, 056 (2021), arXiv: 2011.08023[gr-qc]
- [77]
S. V. M. C. B. Xavier, P. V. P. Cunhaet al., Int. J. Mod. Phys. D29, 2041005 (2020), arXiv: 2003.14349[gr-qc]
- [78]
M. Zhang and J. Jiang, Nucl. Phys. B964, 115313 (2021), arXiv: 2004.03367[gr-qc]
- [79]
M. Zhang and J. Jiang, Phys. Rev. D102, 124012 (2020), arXiv: 2004.11087[gr-qc]
- [80]
A. Belhaj, A. El Balali, W. El Hadriet al., Int. J. Geom. Meth. Mod. Phys.17, 2050169 (2020), arXiv: 2007.16083[hep-th]
- [81]
A. Carleo, G. Lambiase, and L. Mastrototaro, Eur. Phys. J. C82, 776 (2022), arXiv: 2206.12988[gr-qc]
- [82]
W. Heisenberg and H. Euler, Z. Phys.98, 714 (1936), arXiv: physics/0605038
- [83]
M. Kalb and P. Ramond, Phys. Rev. D9, 2273 (1974)
- [84]
L. A. Lessa, J. E. G. Silva, R. V. Malufet al., Eur. Phys. J. C80, 335 (2020), arXiv: 1911.10296[gr-qc]
- [85]
M. A. Raza, M. Zubair, and E. Maqsood, JCAP05, 047 (2024), arXiv: 2401.04779[gr-qc]
- [86]
M. Zubair, M. A. Raza, and E. Maqsood, Phys. Dark Univ.42, 101334 (2023), arXiv: 2310.12325[gr-qc]
- [87]
G. W. Gibbons and K.-i. Maeda, Nucl. Phys. B298, 741 (1988)
- [88]
D. Garfinkle, G. T. Horowitz, and A. Strominger, Phys. Rev. D43, 3140 (1991)
- [89]
G. T. Horowitz and A. Strominger, Nucl. Phys. B360, 197 (1991)
- [90]
A. D. Shapere, S. Trivedi, and F. Wilczek, Mod. Phys. Lett. A6, 2677 (1991)
- [91]
J. L. Synge, ed.,Relativity: The General theory(1960)
- [92]
V. Perlick, O. Y. Tsupko, and G. S. Bisnovatyi-Kogan, Phys. Rev. D92, 104031 (2015), arXiv: 1507.04217[gr-qc]
- [93]
F. Atamurotov, K. Jusufi, M. Jamilet al., Phys. Rev. D104, 064053 (2021), arXiv: 2109.08150[gr-qc]
- [94]
M. A. Raza, J. Rayimbaev, F. Sarikulovet al., Phys. Dark Univ.44, 101488 (2024), arXiv: 2311.15784[gr-qc]
- [95]
B. BEZDĚKOVÁ,Electromagnetic Waves in Dispersiveand Refractive Relativistic Systems, Master's thesis, Diplomová práce, vedoucí Bičák, Jiří. Praha: Univerzita Karlova, Matematicko-fyzikální fakulta, Ústav teoretické fyziky, (2019)
- [96]
B. Turimov, B. Ahmedov, A. Abdujabbarovet al., Int. J. Mod. Phys. D28, 2040013 (2019), arXiv: 1802.03293[gr-qc]
- [97]
V. S. Morozova, B. J. Ahmedov, and A. A. Tursunov, Astrophys. Space Sci.346, 513 (2013)
- [98]
A. A. A. Filho, (2024), arXiv: 2406.11582[gr-qc]
- [99]
M. Fathi, M. Olivares, and J. R. Villanueva, Eur. Phys. J. C80, 51 (2020), arXiv: 1910.12811[gr-qc]
- [100]
K. Yang, Y. Z. Chen, Z. Q. Duanet al., Phys. Rev. D108, 124004 (2023), arXiv: 2308.06613[gr-qc]