• [1]

    The Event Horizon Telescope Collaboration, Astrophys. J. Lett. 875, L1 (2019)

  • [2]

    The Event Horizon Telescope Collaboration, Astrophys. J. Lett. 875, L2 (2019)

  • [3]

    The Event Horizon Telescope Collaboration, Astrophys. J. Lett. 875, L3 (2019)

  • [4]

    The Event Horizon Telescope Collaboration, Astrophys. J. Lett. 875, L4 (2019)

  • [5]

    The Event Horizon Telescope Collaboration, Astrophys. J. Lett. 875, L5 (2019)

  • [6]

    The Event Horizon Telescope Collaboration, Astrophys. J. Lett. 875, L6 (2019)

  • [7]

    H. Falcke, F. Melia, and E. Agol, Astrophys. J. Lett. 528, L13 (2000)

  • [8]

    F. Melia, and H. Falcke, Annu. Rev. Astron. Astrophys. 39, 309 (2001)

  • [9]

    M. Shahzadi, G. Lukes-Gerakopoulos, and M. Kološ, Phys. Rev. D 112, 064013 (2025)

  • [10]

    M. Kološ, and M. Shahzadi, in Proceedings of RAGtime 23-25: Workshops on Black Holes and Neutron Stars, 10, 21-27 (2023).

  • [11]

    S. Iftikhar and M. Shahzadi, Eur. Phys. J. C 79, 473 (2019)

  • [12]

    M. Shahzadi, Z. Yousaf, and S. U. Khan, Phys. Dark Univ. 24, 100263 (2019)

  • [13]

    M. Kološ, M. Shahzadi, and A. Tursunov, Eur. Phys. J. C 83, 323 (2023)

  • [14]

    M. Shahzadi, M. Kološ, R. Saleem, Y. Habib, and A. Eduarte-Rojas, Phys. Rev. D 108, 103006 (2023)

  • [15]

    M. Shahzadi, M. Kološ, R. Saleem, and Z. Stuchlík, Class. Quantum Grav. 41, 075014 (2024)

  • [16]

    M. Sharif and M. Shahzadi, J. Exp. Theor. Phys. 127, 491 (2018)

  • [17]

    M. Shahzadi, M. Kološ, Z. Stuchlík, and Y. Habib, Eur. Phys. J. C 82, 407 (2022)

  • [18]

    A.E. Broderick and A. Loeb, Mon. Not. Roy. Astron. Soc. 363, 353 (2005)

  • [19]

    M. Moscibrodzka, C.F. Gammie, J.C. Dolence, H. Shiokawa, and P.K. Leung, Astrophys. J. 706, 497 (2009)

  • [20]

    J. Dexter, E. Agol, and P.C. Fragile, Astrophys. J. Lett. 703, L142 (2009)

  • [21]

    A.E. Broderick, V.L. Fish, S.S. Doeleman, and A. Loeb, Astrophys. J. 735, 110 (2011)

  • [22]

    A.E. Broderick, T. Johannsen, A. Loeb, and D. Psaltis, Astrophys. J. 784, 7 (2014)

  • [23]

    S.E. Gralla, D.E. Holz, and R.M. Wald, Rev. D 100, 024018 (2019)

  • [24]

    R. Narayan, M.D. Johnson, and C.F. Gammie, Astrophys. J. Lett. 885, L33 (2019)

  • [25]

    M.D. Johnson, and A. Lupsasca, Sci. Adv. 6, eaaz1310 (2020)

  • [26]

    T. Bronzwaer, et al., Mon. Not. Roy. Astron. Soc. 501, 4722 (2021)

  • [27]

    P. Kocherlakota, et al., Phys. Rev. D 103, 104047 (2021)

  • [28]

    A.E. Broderick, P. Tiede, D.W. Pesce, and R. Gold, Astrophys. J. 927(1), 6 (2022)

  • [29]

    T. Bronzwaer, and H. Falcke, Astrophys. J. 920(2), 155 (2021)

  • [30]

    M. Calzà, M., Rinaldi, and S. Vagnozzi, Phys. Rev. D 112(10), 104055 (2025)

  • [31]

    M. Calzà, D. Pedrotti, G. W. Yuan, and S. Vagnozzi, arXiv preprint arXiv: 2507.02396 (2025).

  • [32]

    M. Calzà, D. Pedrotti, and S. Vagnozzi, Phys. Rev. D 111(2), 024010 (2025)

  • [33]

    M. Calzà, D. Pedrotti, and S. Vagnozzi, Phys. Rev. D 111(2), 024009.

  • [34]

    M. Calzà, F. Gianesello, M. Rinaldi, and S. Vagnozzi, Sci. Rep. 14(1), 31296 (2024)

  • [35]

    M. Khodadi, S. Vagnozzi, and J. T. Firouzjaee, Sci. Rep. 14(1), 26932 (2024)

  • [36]

    D. Pedrotti, and S. Vagnozzi, Phys. Rev. D 110(8), 084075 (2024)

  • [37]

    S. Vagnozzi, et al., Classical Quantum Gravity 40(16), 165007 (2023)

  • [38]

    Y. Chen, R. Roy, S. Vagnozzi, and L. Visinelli, Phys. Rev. D 106(4), 043021 (2022)

  • [39]

    R. Roy, S. Vagnozzi, and L. Visinelli, Phys. Rev. D 105(8), 083002 (2022)

  • [40]

    M. Khodadi, A. Allahyari, S. Vagnozzi, and D. F. Mota, JCAP 2020(09), 026 (2020)

  • [41]

    S. Vagnozzi, C. Bambi, and L. Visinelli, Classical Quantum Gravity 37(8), 087001 (2020)

  • [42]

    A. Allahyari, M. Khodadi, S. Vagnozzi, and D. F. Mota, JCAP 2020(02), 003 (2020)

  • [43]

    S. Vagnozzi, and L. Visinelli, arXiv preprint arXiv: 1905.12421 (2019).

  • [44]

    C. Bambi, K. Freese, S. Vagnozzi, and L. Visinelli, Phys. Rev. D 100(4), 044057 (2019)

  • [45]

    S. Aktar, N. U. Molla, F. Rahaman, and G. Mustafa, J. High Energy Astrophys. 47, 100385 (2025)

  • [46]

    S. Kiroriwal, S. K. Maurya, J. Kumar, A. Errehymy, G. Mustafa, and K. Myrzakulov, Chin. J. Phys. 95, 404 (2025)

  • [47]

    P. Mukherjee, U., Debnath, H. Chaudhary, and G. Mustafa, JCAP 2025(05), 085 (2025)

  • [48]

    Y. Pahlavon, F. Atamurotov, A. Bouzenada, A. Abdujabbarov, and G. Mustafa, Nucl. Phys. B 1014, 116882 (2025)

  • [49]

    H. Chaudhary, U. Debnath, S. K. Pacif, and G. Mustafa, Ann. Phys. 537(5), 2400421 (2025)

  • [50]

    X. Wang, W. Lin, G. Mustafa, and G. He, Phys. Rev. D 111(8), 084009 (2025)

  • [51]

    S. K. Maurya, A. Errehymy, K. N. Singh, G. Mustafa, and S. Ray, JCAP 2025(04), 004 (2025)

  • [52]

    G. Rakhimova, F. Abdulkhamidov, F. Atamurotov, A. Abdujabbarov, and G. Mustafa, Chin. J. Phys. 94, 66 (2025)

  • [53]

    G. Fatima, T. Zhu, F. Javed, A. Waseem, and G. Mustafa, Eur. Phys. J. C 85(2), 208 (2025)

  • [54]

    G. Fatima, F. Javed, A. Waseem, B. Almutairi, G. Mustafa, F. Atamurotov, and E. Güdekli, Phys. Dark Universe 47, 101820 (2025)

  • [55]

    F. Javed, S. Shaukat, G. Mustafa, A. Ditta, and B. Almutairi, Phys. Dark Universe 47, 101826 (2025)

  • [56]

    G. Mustafa, F. Javed, S. K. Maurya, A. Abd-Elmonem, F. Atamurotov, N. Alhubieshi, and P. Channuie, Phys. Dark Universe 47, 101825 (2025)

  • [57]

    N. U. Molla, H. Chaudhary, S. Capozziello, F. Atamurotov, G. Mustafa, and U. Debnath, Phys. Dark Universe 47, 101804 (2025)

  • [58]

    G. Fatima, F. Javed, G. Mustafa, and F. Tchier, Int. J. Geom. Methods Mod. Phys. 22(02), 2450279 (2025)

  • [59]

    H. Chaudhary, S. K. J. Pacif, G. Mustafa, F. Atamurotov, and F. Javed, J. High Energy Astrophys. 45, 340 (2025)

  • [60]

    A. Ditta, G. Mustafa, and A. Mahmood, J. High Energy Astrophys. 45, 350 (2025)

  • [61]

    G. Mustafa, S. K. Maurya, T. Naseer, A. Cilli, A. Güdekli, E. Abd-Elmonem, and N. Alhubieshi, Nucl. Phys. B 1012, 116812 (2025)

  • [62]

    B. Rasheed, A. Ditta, T. Naseer, F. Javed, and G. Mustafa, Int. J. Geom. Methods Mod. Phys. 22(04), 2450302 (2025)

  • [63]

    M. K. Jasim, S. K. Maurya, S. Ray, and G. Mustafa, Int. J. Geom. Methods Mod. Phys. 24, 2550123 (2025)

  • [64]

    A. Hussain, F. Javed, G. Fatima, F. Tchier, S. Nozima, and G. Mustafa, Int. J. Geom. Methods Mod. Phys. 22(03), 2450297 (2025)

  • [65]

    N. Arkani-Hamed, S. Dimopoulos, G. Dvali, and G. Gabadadze, arXiv:hep-th/0209227 (2002).

  • [66]

    S. Nojiri, and S. D. Odintsov, Phys. Lett. B 659, 821 (2008)

  • [67]

    G. Calcagni, M. Montobbio, and G. Nardelli, Phys. Rev. D 76, 126001 (2007)

  • [68]

    T. Biswas, E. Gerwick, T. Koivisto, and A. Mazumdar, Phys. Rev. Lett. 108, 031101 (2012)

  • [69]

    S. Park, and S. Dodelson, Phys. Rev. D 87, 024003 (2013)

  • [70]

    M. Maggiore, and M. Mancarella, Phys. Rev. D 90, 023005 (2014)

  • [71]

    Y. Dirian, S. Foffa, N. Khosravi, M. Kunz, and M. Maggiore, JCAP 06, 033 (2014)

  • [72]

    S. Capozziello, R. D’Agostino, and O. Luongo, Phys. Lett. B 834, 137475 (2022)

  • [73]

    C. Deffayet, and R. P. Woodard, JCAP 05, 042 (2024)

  • [74]

    L. Modesto, Phys. Rev. D 86, 044005 (2012)

  • [75]

    L. Modesto, and L. Rachwał, Int. J. Mod. Phys. D 26, 1730020 (2017)

  • [76]

    S. Deser, and R. P. Woodard, Phys. Rev. Lett. 99, 111301 (2007)

  • [77]

    E. Belgacem, A. Finke, A. Frassino, and M. Maggiore, JCAP 02, 035 (2019)

  • [78]

    S. Deser, and R. P. Woodard, JCAP 06, 034 (2019)

  • [79]

    J.-C. Ding, and J.-B. Deng, JCAP 12, 054 (2019)

  • [80]

    C.-Y. Chen, P. Chen, and S. Park, Phys. Lett. B 796, 112 (2019)

  • [81]

    D. Jackson, and R. Bufalo, JCAP 05, 043 (2022)

  • [82]

    S. Capozziello, and R. D’Agostino, Phys. Dark Univ. 42, 101346 (2023)

  • [83]

    D. Jackson, and R. Bufalo, JCAP 05, 010 (2023)

  • [84]

    C.-Y. Chen, and S. Park, Phys. Rev. D 103, 064029 (2021)

  • [85]

    A. Kehagias, and M. Maggiore, JHEP 08, 029 (2014)

  • [86]

    G. Calcagni, L. Modesto, and Y. S. Myung, Phys. Lett. B 783, 19 (2018)

  • [87]

    U. Kumar, S. Panda, and A. Patel, Eur. Phys. J. C 80, 614 (2020)

  • [88]

    L. Buoninfante, B. L. Giacchini, and T. de Paula Netto, arXiv:2211.03497 [gr-qc] (2024).

  • [89]

    R. D’Agostino, V. De Falco, Phys. Rev. D 112(6), 064028 (2025)

  • [90]

    J. Rayimbaev, P. Tadjimuratov, A. Abdujabbarov, B. Ahmedov, and M. Khudoyberdieva, Galaxies 9(4), 75 (2021)

  • [91]

    S. Jumaniyozov, M. Zahid, M. Alloqulov, I. Ibragimov, J. Rayimbaev and S. Murodov, Eur. Phys. J. C 85, 126 (2025)

  • [92]

    S. Faraji, Astron. Rep. 67, S207 (2023)

  • [93]

    Z. Stuchlík, and J. Vrba, JCAP 2021(11), 059 (2021)

  • [94]

    J. Homan, et al., Astrophys. J. 586, 1262 (2003)

  • [95]

    J. Rayimbaev, B. Ahmedov, and A.H. Bokhari, Int. J. Mod. Phys. D 31, 2240004 (2022)

  • [96]

    M. Qi, J. Rayimbaev, and B. Ahmedov, Eur. Phys. J. C 83, 730 (2023)

  • [97]

    L. Rezzolla, and O. Zanotti, Relativistic Hydrodynamics (2013)

  • [98]

    L. Rezzolla, S. Yoshida, T.J. Maccarone, and O. Zanotti, Mon. Not. R. Astron. Soc. 344, L37 (2003)

  • [99]

    G. Torok, A. Kotrlova, E. Sramkova, and Z. Stuchlik, Astron. Astrophys. 531, A59 (2011)

  • [100]

    Z. Stuchlik, A. Kotrlova, and G. Torok, Astron. Astrophys. 525, A82 (2011)

  • [101]

    Z. Stuchlik, A. Kotrlova, and G. Torok, Astron. Astrophys. 552, A10 (2013)

  • [102]

    G. Mustafa, I. Hussain, and W.-M. Liu, Chin. J. Phys. 80, 148 (2022)

  • [103]

    X. Jiang, P. Wang, H. Yang, and H. Wu, Eur. Phys. J. C 81, 1043 (2021)

  • [104]

    L. Amarilla, E.F. Eiroa, and G. Giribet, Phys. Rev. D 81, 124045 (2010)

  • [105]

    Y. Liu, G. Mustafa, S.K. Maurya, and F. Javed, Eur. Phys. J. C 83, 584 (2023)

  • [106]

    Z. Stuchlík, and M. Kološ, Astron. Astrophys. 586, A130 (2016)

  • [107]

    R. A. Remillard, et al., Astrophys. J. 517(2), L127 (1999)

  • [108]

    E. H. Morgan, R. A. Remillard, and J. Greiner, Astrophys. J. 482(2), 993 (1997)

  • [109]

    R. A. Remillard, et al., Astrophys. J. 637(2), 1002 (2006)

  • [110]

    M. Shahzadi, M. Kološ, R. Saleem, and Z. Stuchlík, Classical. Quant. Grav. 41(7), 075014 (2024)

  • [111]

    E. H. Morgan, R. A. Remillard, and J. Greiner, Astrophys. J. 482(2), 993 (1997)

  • [112]

    S. Jumaniyozov, et al., Eur. Phys. J. C 85(2), 126 (2025)

  • [113]

    O. Donmez, Eur. Phys. J. C 84(5), 524 (2024)

  • [114]

    A. Garg, R. Misra, and S. Sen, Mon. Not. R. Astron. Soc. 514(3), 3285 (2022)

  • [115]

    M. Masterson, et al., Nature 638, 370 (2025)

  • [116]

    C. Bambi, JCAP 2012(09), 014 (2012)

  • [117]

    F. Abdulkhamidov, B. Narzilloev, I. Hussain, A. Abdujabbarov, and B. Ahmedov, Eur. Phys. J. C 84(4), 420 (2024)

  • [118]

    G. Török, Astron. Nachr. 326(9), 856 (2005)

  • [119]

    J. Petri, Astrophys. Space Sci. 318(3), 181 (2008)

  • [120]

    F. Vignarca, S. Migliari, T. Belloni, D. Psaltis, and M. Van Der Klis, Astron. Astrophys. 397(2), 729 (2003)

  • [121]

    D. R. Pasham, et al., Astrophys. J/ Lett. 811(1), L11 (2015)

  • [122]

    R. V. Wagoner, Astrophys. J. Lett. 752(2), L18 (2012)

  • [123]

    G. Mustafa, E. Demir, A. Davlataliev, H. Chaudhary, F. Atamurotov, and E. Güdekli, Phys. Dark Universe 46, 101644 (2024)

  • [124]

    J. Rayimbaev, S. Murodov, A. Shermatov, and A. Yusupov, Eur. Phys. J. C 84(10), 1114 (2024)

  • [125]

    C. Bambi, J. Cosmol. Astropart. Phys. 2012, 014 (2012)

  • [126]

    O. Dönmez, Astrophys. Space Sci. 293, 323 (2004)

  • [127]

    P.J. Montero, O. Zanotti, Mon. Not. Roy. Astron. Soc. 419, 1507 (2011)

  • [128]

    M. Shahzadi, M. Kološ, R. Saleem, Z. Stuchlík, Class. Quantum Gravity 41, 075014 (2024)

  • [129]

    Z. Stuchlík, M. Kološ, A. Tursunov, Publ. Astron. Soc. Jpn. 74, 1220 (2022)

  • [130]

    K. Boshkayev, O. Luongo, M. Muccino, Phys. Rev. D 108, 124034 (2023)

  • [131]

    K. Boshkayev, T. Konysbayev, Y. Kurmanov, M. Muccino, H. Quevedo, Mon. Not. Roy. Astron. Soc. 531, 3876 (2024)

  • [132]

    K. Boshkayev, A. Idrissov, O. Luongo, M. Muccino, Phys. Rev. D 108, 044063 (2023)

  • [133]

    S. Mitra, J. Vrba, J. Rayimbaev, Z. Stuchlik, B. Ahmedov, Phys. Dark Univ. 46, 101561 (2024)

  • [134]

    J. Rayimbaev, U. Eshimbetov, B. Majeed, A. Abdujabbarov, A. Abduvokhidov, B. Abdulazizov, A. Xalmirzayev, Chin. Phys. C 48, 055104 (2024)

  • [135]

    F. Abdulkhamidov, P. Nedkova, J. Rayimbaev, J. Kunz, B. Ahmedov, Phys. Rev. D 109, 104074 (2024)

  • [136]

    M. Qi, J. Rayimbaev, B. Ahmedov, Eur. Phys. J. C 83, 730 (2023)

  • [137]

    J. Rayimbaev, A. Abdujabbarov, F. Abdulkhamidov, V. Khamidov, S. Djumanov, J. Toshov, S. Inoyatov, Eur. Phys. J. C 82, 1110 (2022)

  • [138]

    Z. Stuchlík, A. Kotrlová, in RAGtime 8/9: Workshops on Black Holes and Neutron Stars (2007).

  • [139]

    Z. Stuchlík, A. Kotrlová, Gen. Relativ. Gravit. 41, 1305 (2009)

  • [140]

    S. Murodov, K. Badalov, J. Rayimbaev, B. Ahmedov, Z. Stuchlík, Symmetry 16, 109 (2024)

  • [141]

    S. Murodov, J. Rayimbaev, B. Ahmedov, A. Hakimov, Symmetry 15, 2084 (2023)

  • [142]

    U. Nucamendi, R. Becerril, P. Sheoran, Eur. Phys. J. C 80, 35 (2020)

  • [143]

    A.N. Aliev, P. Talazan, Phys. Rev. D 80, 044023 (2009)

  • [144]

    K. Jusufi, M. Jamil, P.H.R.S. Moraes, Eur. Phys. J. C 80, 354 (2020)

  • [145]

    S. Das, E.C. Vagenas, Can. J. Phys. 87, 233 (2018)

  • [146]

    K. Jusufi, M. Azreg-Aïnou, M. Jamil, T. Zhu, Int. J. Geom. Methods Mod. Phys. 19, 2250068 (2022)

  • [147]

    J. Abedi, H. Arfaei, J. Cosmol. Astropart. Phys. 2016, 042 (2016)

  • [148]

    I. Banerjee, J. Cosmol. Astropart. Phys. 2022, 034 (2022)

  • [149]

    S.E. Motta, T.M. Belloni, arXiv: 2307.00867 (2023).

  • [150]

    C.-Y. Shao, C. Zhang, W. Zhang, C.-G. Shao, Phys. Rev. D 109, 064012 (2024)

  • [151]

    K. Nozari, S.H. Mehdipour, Astrophys. Space Sci. 339, 581 (2012)

  • [152]

    P. Nicolini, Int. J. Mod. Phys. A 24, 1229 (2019)

  • [153]

    J. Rayimbaev, A.H. Bokhari, B. Ahmedov, Class. Quantum Gravity 39, 075021 (2022)

  • [154]

    A. Ashraf, et al., Phys. Dark Universe 47, 101787 (2025)

  • [155]

    G. Mustafa, et al., Phys. Dark Universe 47, 101765 (2025)

  • [156]

    G. Mustafa, et al., Phys. Dark Universe 47, 101753 (2025)

  • [157]

    A. Ashraf, et al., Physics of the Dark Universe 48, 101836 (2025)

  • [158]

    A. Ashraf, et al., Phys. Dark Universe 47, 101823 (2025)

  • [159]

    A. Ditta, et al., Phys. Dark Universe 47, 101818 (2025)

  • [160]

    A. Ditta, et al., Phys. Dark Universe 46, 101573 (2024)

  • [161]

    A. Bouzenada, et al., Nucl. Phys. B 1017, 116928 (2025)

  • [162]

    A. Saleem, et al., Nucl. Phys. B 1017, 116926 (2025)

  • [163]

    S. K. Maurya, et al., Nucl. Phys. B 1020, 117139 (2025)

  • [164]

    A. Ditta, et al., Nucl. Phys. B 1019, 117099 (2025)

  • [165]

    B. Turimov, S. Usanov and Y. Khamroev, Physics of the Dark Universe 48, 101876 (2025)