• [1]

    K. Schwarzschild, Sitzungsberichte der Kniglich Preussischen Akademie der Wissenschaften, 189 (1916).

  • [2]

    S. M. Blinder, arXiv: 1512.02061 [physics.pop-ph]

  • [3]

    R. P. Kerr, Phys. Rev. Lett. 11, 237 (1963)

  • [4]

    A. Ashtekar, J. Baez, A. Corichi et al., Phys. Rev. Lett. 80, 904 (1998)

  • [5]

    M. Baryakhtar, Phys. Rev. D 85, 125019 (2012)

  • [6]

    N. E. Bjerrum-Bohr, J. F. Donoghue, and B. R. Holstein, Phys. Rev. D 68, 084005 (2003), arXiv: 0211071[hep-th]

  • [7]

    R. Aros, D. E. Díaz, and A. Montecinos, Phys. Rev. D 88, 104024 (2013)

  • [8]

    A. Ashtekar and J. Pullin, arXiv: 1703.07396 [gr-qc]

  • [9]

    A. Ashtekar and J. Pullin, Loop Quantum Gravity: The First 30 Years 100 Years of General Relativity, Volume 4, Vol. 4 (2017).

  • [10]

    P. Frisoni, arXiv: 2305.12215 [gr-qc]

  • [11]

    E. Witten, Nucl. Phys. B 443, 85 (1995), arXiv: 9503124 [hep-th]

  • [12]

    D. Lüst, P. Mayr, R. Richter et al., Nucl. Phys. B 696, 205 (2004)

  • [13]

    M. Maggiore, Phys. Lett. B 304, 65 (1993), arXiv: 9301067 [gr-qc]

  • [14]

    S. Das and E. C. Vagenas, Phys. Rev. Lett. 101, 221301 (2008)

  • [15]

    A. Ashtekar and J. Lewandowski, Class. Quant. Grav. 21, R53 (2004), arXiv: 0404018 [gr-qc]

  • [16]

    P. Singh and A. Toporensky, Phys. Rev. D 69, 104008 (2004), arXiv: 0312110 [gr-qc]

  • [17]

    A. Ashtekar, T. Pawlowski, and P. Singh, Phys. Rev. D 74, 084003 (2006), arXiv: 0607039 [gr-qc]

  • [18]

    A. Ashtekar, T. Pawlowski, and P. Singh, Phys. Rev. Lett. 96, 141301 (2006), arXiv: 0602086 [gr-qc]

  • [19]

    G. Date and G. M. Hossain, Phys. Rev. Lett. 94, 011302 (2005), arXiv: 0407074 [gr-qc]

  • [20]

    A. Ashtekar and P. Singh, Class. Quant. Grav. 28, 213001 (2011), arXiv: 1108.0893 [gr-qc]

  • [21]

    T. Papanikolaou, Class. Quant. Grav. 40, 134001 (2023), arXiv: 2301.11439 [gr-qc]

  • [22]

    B. F. Li and P. Singh, arXiv: 2304.05426 [gr-qc]

  • [23]

    L. Modesto, Int. J. Theor. Phys. 49, 1649 (2010), arXiv: 0811.2196 [gr-qc]

  • [24]

    L. Modesto and I. Prémont-Schwarz, Phys. Rev. D 80, 064041 (2009), arXiv: 0905.3170 [hep-th]

  • [25]

    S. Sahu, K. Lochan, and D. Narasimha, Phys. Rev. D 91, 063001 (2015), arXiv: 1502.05619 [gr-qc]

  • [26]

    A. Ashtekar, J. Olmedo, and P. Singh, Phys. Rev. Lett. 121, 241301 (2018), arXiv: 1806.00648 [gr-qc]

  • [27]

    A. Ashtekar, J. Olmedo, and P. Singh, Phys. Rev. D 98, 126003 (2018), arXiv: 1806.02406 [gr-qc]

  • [28]

    M. Bojowald, S. Brahma, and D. h. Yeom, Phys. Rev. D 98, 046015 (2018), arXiv: 1803.01119 [gr-qc]

  • [29]

    E. Alesci, S. Bahrami, and D. Pranzetti, Phys. Lett. B 797, 134908 (2019), arXiv: 1904.12412 [gr-qc]

  • [30]

    M. Assanioussi, A. Dapor, and K. Liegener, Phys. Rev. D 101, 026002 (2020), arXiv: 1908.05756 [gr-qc]

  • [31]

    N. Bodendorfer, F. M. Mele, and J. Münch, Phys. Lett. B 819, 136390 (2021), arXiv: 1911.12646 [gr-qc]

  • [32]

    A. Ashtekar, Universe 6, 21 (2020), arXiv: 2001.08833 [gr-qc]

  • [33]

    W. C. Gan, N. O. Santos, F. W. Shu et al., Phys. Rev. D 102, 124030 (2020), arXiv: 2008.09664 [gr-qc]

  • [34]

    A. Perez, Rep. Prog. Phys. 80, 126901 (2017), arXiv: 1703.09149 [gr-qc]

  • [35]

    Y. C. Liu, J. X. Feng, F. W. Shu et al., Phys. Rev. D 104, 106001 (2021), arXiv: 2109.02861 [gr-qc]

  • [36]

    Q. M. Fu and X. Zhang, Phys. Rev. D 105, 064020 (2022), arXiv: 2111.07223 [gr-qc]

  • [37]

    S. Brahma, C. Y. Chen, and D. h. Yeom, Phys. Rev. Lett. 126, 181301 (2021), arXiv: 2012.08785 [gr-qc]

  • [38]

    S. Yang, W. D. Guo, Q. Tan et al., Phys. Rev. D 108, 024055 (2023), arXiv: 2304.06895 [gr-qc]

  • [39]

    J. M. Yan, C. Liu, T. Zhu et al., Phys. Rev. D 107, 084043 (2023), arXiv: 2302.10482 [gr-qc]

  • [40]

    S. Albuquerque, I. P. Lobo, and V. B. Bezerra, Class. Quant. Grav. 40, 174001 (2023), arXiv: 2301.07746 [gr-qc]

  • [41]

    H. X. Jiang, C. Liu, I. K. Dihingia et al., JCAP 01, 059, arXiv: 2312.04288 [gr-qc]

  • [42]

    H. Jiang, M. Alloqulov, Q. Wu et al., Phys. Dark Univ. 46, 101627 (2024)

  • [43]

    L. You, Y. H. Feng, R. B. Wang et al., Universe 10, 393 (2024)

  • [44]

    S. H. Dong, F. Hosseinifar, F. Studnička et al., Phys. Lett. B 860, 139182 (2025)

  • [45]

    H. Gong, S. Li, D. Zhang et al., Phys. Rev. D 110, 044040 (2024)

  • [46]

    L. Zhao, M. Tang, and Z. Xu, Eur. Phys. J. C 84, 971 (2024), arXiv: 2403.18606 [gr-qc]

  • [47]

    B. Czerny, S. Cao, V. K. Jaiswal et al., Astrophys. Space Sci. 368, 8 (2023), arXiv: 2209.06563 [astro-ph.GA]

  • [48]

    C. W. Morgan, C. S. Kochanek, N. D. Morgan et al., Astrophys. J. 712, 1129 (2010), arXiv: 1002.4160 [astro-ph.CO]

  • [49]

    Q. Bu and S. Zhang, Black holes: Accretion processes in x-ray binaries, in Handbook of X-ray and Gamma-ray Astrophysics (Springer Nature Singapore, 2023) p. 1–28.

  • [50]

    J. Schultz, Studies of accretion disks in X-ray binaries, Ph.D. thesis, (Finland: University of Helsinki, 2005)

  • [51]

    Y. Yao, S. N. Zhang, and X. Zhang, AIP Conf. Proc. 587, 106 (2001)

  • [52]

    B. M. Peterson, An Introduction to Active Galactic Nuclei (1997).

  • [53]

    J. C. McKinney and R. Narayan, Mon. Not. Roy. Astron. Soc. 375, 531 (2007)

  • [54]

    A. Ashtekar and M. Bojowald, Class. Quant. Grav. 23, 391 (2006)

  • [55]

    S. B. Giddings, Phys. Rev. D 46, 1347 (1992)

  • [56]

    S. B. Giddings, Phys. Rev. D 49, 947 (1994)

  • [57]

    C. Rovelli, Quantum Gravity (Cambridge University Press, 2004).

  • [58]

    I. D. Novikov and K. S. Thorne, Astrophysics of black holes, (Gordon and Breach, Science Publishers, Inc, United States, 1973).

  • [59]

    K. S. Thorne, Astrophys. J. 191, 507 (1974)

  • [60]

    J. R. Oppenheimer and H. Snyder, Phys. Rev. 56, 455 (1939)

  • [61]

    J. Lewandowski, Y. Ma, J. Yang et al., Phys. Rev. Lett. 130, 101501 (2023)

  • [62]

    S. Yang, Y. P. Zhang, T. Zhu et al., arXiv: 2407.00283 [gr-qc]

  • [63]

    A. Perez and C. Rovelli, Phys. Rev. D 73, 044013 (2006)

  • [64]

    D. N. Page and K. S. Thorne, Astrophys. J. 191, 499 (1974)

  • [65]

    C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (W. H. Freeman, San Francisco, 1973).

  • [66]

    S. L. Shapiro and S. A. Teukolsky, Black Holes, White Dwarfs, and Neutron Stars (John Wiley & Sons, New York, 1983).

  • [67]

    S. Shaymatov, P. Sheoran, and S. Siwach, Phys. Rev. D 105, 104059 (2022), arXiv: 2110.10610 [gr-qc]

  • [68]

    S. Shaymatov, P. Sheoran, R. Becerril et al., Phys. Rev. D 106, 024039 (2022)

  • [69]

    N. I. Shakura and R. A. Sunyaev, Astron. Astrophys. 24, 337 (1973)

  • [70]

    K. Boshkayev, A. Idrissov, O. Luongo et al., Mon. Not. Roy. Astron. Soc. 496, 1115 (2020), arXiv: 2006.01269 [astro-ph.HE]

  • [71]

    B. Narzilloev and B. Ahmedov, Symmetry 14, 1765 (2022)

  • [72]

    S. Shaymatov, K. Jusufi, M. Alloqulov et al., Eur. Phys. J. Plus 138, 997 (2023)

  • [73]

    M. Alloqulov, S. Shaymatov, B. Ahmedov et al., Chin. Phys. C 48, 025101 (2024)

  • [74]

    K. Boshkayev, T. Konysbayev, E. Kurmanov et al., Phys. Rev. D 104, 084009 (2021)

  • [75]

    K. Boshkayev, T. Konysbayev, Y. Kurmanov et al., Eur. Phys. J. C 84, 230 (2024), arXiv: 2307.15003 [gr-qc]

  • [76]

    Y. Kurmanov, K. Boshkayev, T. Konysbayev et al., Phys. Dark Univ. 46, 101566 (2024), arXiv: 2404.15437 [gr-qc]

  • [77]

    M. Alloqulov and S. Shaymatov, Eur. Phys. J. Plus 139, 731 (2024), arXiv: 2408.00035 [gr-qc]

  • [78]

    U. Uktamov, M. Alloqulov, S. Shaymatov et al., Phys. Dark Univ. 47, 101743 (2025)

  • [79]

    M. Alloqulov, A. Abdujabbarov, B. Ahmedov et al., Eur. Phys. J. C 85, 786 (2025)

  • [80]

    M. Alloqulov, M. Jamil, S. Shaymatov et al., JHEAp 48, 100424 (2025)