-
[1]
K. Akiyama et al. (Event Horizon Telescope Collaboration), Astrophys. J. Lett. 875, L1 (2019), arXiv: 1906.11238 [astro-ph.GA]
-
[2]
K. Akiyama et al. (Event Horizon Telescope Collaboration), Astrophys. J. Lett. 875, L4 (2019), arXiv: 1906.11241 [astro-ph.GA]
-
[3]
K. Akiyama et al. (Event Horizon Telescope Collaboration), Astrophys. J. Lett. 930, L12 (2022), arXiv: 2311.08680 [astro-ph.HE]
-
[4]
B. P. Abbott and others (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. Lett. 116, 061102 (2016), arXiv: 1602.03837[gr-qc]
-
[5]
A. Duran-Cabacxes, D. Rubiera-Garcia, and D. SxaezChillxon Gxomez, Phys. Rev. D 112, 044016 (2025), arXiv: 2506.10814[gr-qc]
-
[6]
M. Guerrero, G. J. Olmo, D. Rubiera-Garcia et al., JCAP (08), 036 (2021), arXiv: 2105.15073[grqc]
-
[7]
G. J. Olmo, J. L. Rosa, D. Rubiera-Garcia et al., Class. Quant. Grav. 40, 174002 (2023), arXiv: 2302.12064[gr-qc]
-
[8]
S. E. Gralla, D. E. Holz, and R. M. Wald, Phys. Rev. D 100, 024018 (2019), arXiv: 1906.00873[astroph.HE]
-
[9]
R. Penrose, Phys. Rev. Lett. 14, 57 (1965)
-
[10]
M. Reuter, Phys. Rev. D 57, 971 (1998), arXiv: hepth/9605030
-
[11]
M. Niedermaier and M. Reuter, Living Reviews in Relativity 9, 5 (2006)
-
[12]
M. Reuter and F. Saueressig, Quantum Gravity and the Functional Renormalization Group: The Road towards Asymptotic Safety, (Cambridge University Press, 2019)
-
[13]
A. Bonanno and M. Reuter, Phys. Rev. D 62, 043008 (2000), arXiv: hep-th/0002196
-
[14]
A. Bonanno and M. Reuter, Phys. Rev. D 73, 083005 (2006), arXiv: hep-th/0602159
-
[15]
K. Falls, C. R. King, D. F. Litim et al., Phys. Rev. D 97, 086006 (2018), arXiv: 1801.00162[hep-th]
-
[16]
G. Alencar, T. M. Crispim, C. R. Muniz et al., (2026), arXiv: 2603.05130v1[gr-qc]
-
[17]
J. L. Synge, Relativity: The General Theory (NorthHolland, Amsterdam, 1960)
-
[18]
V. Perlick, Living Reviews in Relativity 7, 9 (2004)
-
[19]
O. Y. Tsupko and G. S. Bisnovatyi-Kogan, MNRAS 427, 2017 (2012)
-
[20]
G. S. Bisnovatyi-Kogan and O. Y. Tsupko, MNRAS 404, 1790 (2010), arXiv: 1006.2321[astro-ph.CO]
-
[21]
F. Feleppa, V. Bozza, and O. Y. Tsupko, Phys. Rev. D 110, 064031 (2024)
-
[22]
F. Feleppa, V. Bozza, and O. Y. Tsupko, Phys. Rev. D 111, 044018 (2025)
-
[23]
F. Feleppa, F. Aratore, and V. Bozza, Phys. Rev. D 112, 1 (2025)
-
[24]
V. Perlick, O. Y. Tsupko, and G. S. Bisnovatyi-Kogan, Phys. Rev. D 92, 104031 (2015)
-
[25]
J. L. Synge, MNRAS131, 463 (1966)
-
[26]
V. Bozza, Phys. Rev. D 66, 103001 (2002), arXiv: gr-qc/0208075
-
[27]
A. Rogers, MNRAS 451, 17 (2015)
-
[28]
V. S. Morozova, B. J. Ahmedov, and A. A. Tursunov, Astrophys. Space Sci. 346, 513 (2013)
-
[29]
A. Abdujabbarov, B. Toshmatov, Z. Stuchlxık et al., Int. J. Mod. Phys. D 25, 1650023 (2015)
-
[30]
M. Alloqulov, S. Shaymatov, A. Jawad et al., Commun. Theor. Phys. 77, 015402 (2025)
-
[31]
A. Al-Badawi, M. Alloqulov, S. Shaymatov et al., Chin. Phys. C 48, 095105 (2024)
-
[32]
M. Alloqulov, F. Atamurotov, A. Abdujabbarov et al., Chin. Phys. C 47, 075103 (2023)
-
[33]
H. Jiang, M. Alloqulov, Q. Wu et al., Phys. Dark Univ. 46, 101627 (2024)
-
[34]
M. Alloqulov, F. Atamurotov, A. Abdujabbarov et al., Chin. Phys. C 48, 115116 (2024)
-
[35]
A. Al-Badawi, S. Shaymatov, M. Alloqulov et al., Commun. Theor. Phys. 76, 085401 (2024)
-
[36]
M. Alloqulov, F. Atamurotov, A. Abdujabbarov et al., Chin. Phys. C 48, 025104 (2024)
-
[37]
F. Atamurotov, M. Alloqulov, A. Abdujabbarov et al., Eur. Phys. J. Plus 137, 634 (2022)
-
[38]
J. Sharipov, M. Alloqulov, P. Sheoran et al., Chin. J Phys. 99, 461 (2026)
-
[39]
M. Alloqulov, Y. Isaqjonov, S. Shaymatov et al., Chin. Phys. C 49, 045104 (2025)
-
[40]
J. Khasanov, M. Alloqulov, P. Sheoran et al., JCAP 12, 023 (2025)
-
[41]
W. Javed, I. Hussain, and A. Övgün, Eur. Phys. J. Plus 137, 148 (2022), arXiv: 2201.09879[gr-qc]
-
[42]
F. Atamurotov, I. Hussain, G. Mustafa et al., Chin. Phys. C 47, 025102 (2023)
-
[43]
B. Turimov, O. Rahimov, A. Davlataliev et al., Phys. Dark Univ. 48, 101855 (2025), arXiv: 2502.11210[gr-qc]
-
[44]
A. Davlataliev, B. Narzilloev, I. Hussain et al., Phys. Dark Univ. 42, 101340 (2023)
-
[45]
A. Chowdhuri and A. Bhattacharyya, Phys. Rev. D 104, 064039 (2021)
-
[46]
E. Battista, S. Capozziello, and C. Y. Chen, (2026), arXiv: 2601.10806[gr-qc]
-
[47]
K. S. Virbhadra, Phys. Rev. D 109, 124004 (2024), arXiv: 2402.17190[gr-qc]
-
[48]
K. S. Virbhadra, Can. J. Phys. 102, 523 (2024), arXiv: 2204.01792[gr-qc]
-
[49]
S. L. Adler and K. S. Virbhadra, Gen. Rel. Grav. 54, 93 (2022), arXiv: 2205.04628[gr-qc]
-
[50]
K. S. Virbhadra, Phys. Rev. D 106, 064038 (2022), arXiv: 2204.01879[gr-qc]
-
[51]
K. S. Virbhadra and C. R. Keeton, Phys. Rev. D 77, 124014 (2008), arXiv: 0710.2333[gr-qc]
-
[52]
K. S. Virbhadra, Phys. Rev. D 79, 083004 (2009), arXiv: 0810.2109[gr-qc]
-
[53]
K. S. Virbhadra, D. Narasimha, and S. M. Chitre, Astron. Astrophys. 337, 1 (1998), arXiv: astro-ph/9801174
-
[54]
C. M. Claudel, K. S. Virbhadra, and G. F. R. Ellis, J. Math. Phys. 42, 818 (2001), arXiv: gr-qc/0005050
-
[55]
K. S. Virbhadra and G. F. R. Ellis, Phys. Rev. D 65, 103004 (2002)
-
[56]
K. S. Virbhadra and G. F. R. Ellis, Phys. Rev. D 62, 084003 (2000), arXiv: astro-ph/9904193
-
[57]
Y. Mizuno, Z. Younsi, C. M. Fromm et al., Nature Astron. 2, 585 (2018), arXiv: 1804.05812[astro-ph.GA]
-
[58]
M. Zhang, Y. Mizuno, C. M. Fromm et al., Astron. Astrophys. 687, A88 (2024), arXiv: 2404.04033[astro-ph.HE]
-
[59]
Y. Song, Y. Hou, L. Huang, and B. Chen, Phys. Rev. D 113, 043054 (2026), arXiv: 2507.23281[astro-ph.HE]
-
[60]
K. Moriyama, A. Cruz-Osorio, Y. Mizuno et al., Astron. Astrophys. 694, A135 (2025), arXiv: 2501.08720[astro-ph.HE]
-
[61]
A. Chael, Mon. Not. Roy. Astron. Soc. 532, 3198 (2024), arXiv: 2404.01471[astro-ph.HE]
-
[62]
P. Kocherlakota and L. Rezzolla, Mon. Not. Roy. Astron. Soc. 513, 1229 (2022), arXiv: 2201.05641[gr-qc]
-
[63]
C. M. Fromm et al., Astron. Astrophys. 660, A107 (2022), arXiv: 2111.02518[astro-ph.HE]
-
[64]
D. Bardiev, Y. Wang, M. Kološ et al., Astrophys. J. 972, 55 (2024)
-
[65]
D. Bardiev, J. Schee, and Z. Stuchlxık, Astrophys. J. 993, 62 (2025)
-
[66]
O. Y. Tsupko and G. S. Bisnovatyi-Kogan, Gravit. Cosmol. 15, 184 (2009)
-
[67]
S. Chandrasekhar, The Mathematical Theory of Black Holes (Oxford University Press, 1983)
-
[68]
G. Z. Babar, F. Atamurotov, and A. Z. Babar, Physics of the Dark Universe 32, 100798 (2021)
-
[69]
S. Vxazquez and E. Esteban, Il Nuovo Cimento B 119, 489 (2004)
-
[70]
C. Bambi, K. Freese, S. Vagnozzi et al., Phys. Rev. D 100, 044057 (2019)
-
[71]
K. Akiyama et al. (Event Horizon Telescope Collaboration), Astron. Astrophys. 681, A79 (2024)
-
[72]
M. De Laurentis and P. Salucci, Astrophys. J. 929, 17 (2022), arXiv: 2206.01997[astro-ph.CO]
-
[73]
R. Abuter et al. (GRAVITY), Astron. Astrophys. 636, L5 (2020), arXiv: 2004.07187[astro-ph.GA]
-
[74]
A. Rogers, Mon. Not. Roy. Astron. Soc. 451, 17 (2015), arXiv: 1505.06790[gr-qc]
-
[75]
X. Er and A. Rogers, Mon. Not. Roy. Astron. Soc. 475, 867 (2017), arXiv: 1712.06900[astro-ph.GA]
-
[76]
P. Goldreich and W. H. Julian, Astrophys. J. 157, 869 (1969)
-
[77]
F. Atamurotov, A. Abdujabbarov, and J. Rayimbaev, Eur. Phys. J. C 81, 118 (2021)
-
[78]
O. Y. Tsupko and G. S. Bisnovatyi-Kogan, Plasma Physics Reports 41, 562 (2015)
-
[79]
P. Schneider, J. Ehlers, and E. E. Falco, Gravitational Lenses, Astronomy and Astrophysics Library (Heidelberg: Springer Berlin,1992)
-
[80]
F. Atamurotov, K. Jusufi, M. Jamil et al., Phys. Rev. D 104, 064053 (2021), arXiv: 2109.08150[gr-qc]