• [1]

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

  • [2]

    S. M. Blinder, arXiv e-prints, arXiv: 1512.02061 (2015), arXiv: 1512.02061 [physics.pop-ph].

  • [3]

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

  • [4]

    A. Ashtekar, J. Baez, A. Corichi, and K. Krasnov, 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: hep-th/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 e-prints, arXiv: 1703.07396 (2017), 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 e-prints, arXiv: 2305.12215 (2023), arXiv: 2305.12215 [gr-qc].

  • [11]

    E. Witten, Nuclear Physics B 443, 85 (1995), arXiv: hep-th/9503124 [hep-th]

  • [12]

    D. Lüst, P. Mayr, R. Richter, and S. Stieberger, Nuclear Physics B 696, 205 (2004)

  • [13]

    M. Maggiore, Physics Letters B 304, 65 (1993), arXiv: hep-th/9301067 [gr-qc]

  • [14]

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

  • [15]

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

  • [16]

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

  • [17]

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

  • [18]

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

  • [19]

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

  • [20]

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

  • [21]

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

  • [22]

    B.-F. Li and P. Singh, arXiv e-prints, arXiv: 2304.05426 (2023), 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, and A. Wang, 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, and A. Wang, 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, and Y.-X. Liu, Phys. Rev. D 108, 024055 (2023), arXiv: 2304.06895 [gr-qc]

  • [39]

    J.-M. Yan, C. Liu, T. Zhu, Q. Wu, and A. Wang, 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, Y. Mizuno, H. Xu, T. Zhu, and Q. Wu, JCAP 01, 059, arXiv: 2312.04288 [gr-qc]

  • [42]

    H. Jiang, M. Alloqulov, Q. Wu, S. Shaymatov, and T. Zhu, Phys. Dark Universe 46, 101627 (2024)

  • [43]

    L. You, Y.-H. Feng, R.-B. Wang, X.-R. Hu, and J.-B. Deng, Universe 10, 10.3390/universe10100393 (2024).

  • [44]

    S.-H. Dong, F. Hosseinifar, F. Studnička, and H. Hassanabadi, Physics Letters B 860, 139182 (2025)

  • [45]

    H. Gong, S. Li, D. Zhang, G. Fu, and J.-P. Wu, Phys. Rev. D 110, 044040 (2024)

  • [46]

    L. Zhao, M. Tang, and Z. Xu, European Physical Journal C 84, 971 (2024), arXiv: 2403.18606 [gr-qc]

  • [47]

    B. Czerny, S. Cao, V. K. Jaiswal, V. Karas, N. Khadka, M. L. Martínez-Aldama, M. H. Naddaf, S. Panda, F. Pozo Nuñez, R. Prince, B. Ratra, M. Sniegowska, Z. Yu, and M. Zajaček, Astrophysics and Space Science 368, 8 (2023), arXiv: 2209.06563 [astro-ph.GA]

  • [48]

    C. W. Morgan, C. S. Kochanek, N. D. Morgan, and E. E. Falco, 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, University of Helsinki, Finland (2005).

  • [51]

    Y. Yao, S. N. Zhang, and X. Zhang, in Gamma 2001: Gamma-Ray Astrophysics, American Institute of Physics Conference Series, Vol. 587, edited by S. Ritz, N. Gehrels, and C. R. Shrader (AIP, 2001) pp. 106–110, arXiv: astro-ph/0105537 [astro-ph].

  • [52]

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

  • [53]

    J. C. McKinney and R. Narayan, Monthly Notices of the Royal Astronomical Society 375, 531 (2007)

  • [54]

    A. Ashtekar and M. Bojowald, Classical and Quantum Gravity 23, 391 (2005)

  • [55]

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

  • [56]

    S. B. Giddings, Physical Review 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, and C. Zhang, Phys. Rev. Lett. 130, 101501 (2023)

  • [62]

    S. Yang, Y.-P. Zhang, T. Zhu, L. Zhao, and Y.-X. Liu, Gravitational waveforms from periodic orbits around a quantum-corrected black hole (2024), arXiv: 2407.00283 [gr-qc].

  • [63]

    A. Perez and C. Rovelli, Physical Review D 73, 10.1103/physrevd.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, U. Nucamendi, and B. Ahmedov, 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, and D. Malafarina, Mon. Not. Roy. Astron. Soc. 496, 1115 (2020), arXiv: 2006.01269 [astro-ph.HE]

  • [71]

    B. Narzilloev and B. Ahmedov, Symmetry 14, 10.3390/sym14091765 (2022).

  • [72]

    S. Shaymatov, K. Jusufi, M. Alloqulov, and B. Ahmedov, The European Physical Journal Plus 138, 997 (2023)

  • [73]

    M. Alloqulov, S. Shaymatov, B. Ahmedov, and A. Jawad, Chinese Physics C 48, 025101 (2024)

  • [74]

    K. Boshkayev, T. Konysbayev, E. Kurmanov, O. Luongo, D. Malafarina, and H. Quevedo, Phys. Rev. D 104, 10.1103/physrevd.104.084009 (2021).

  • [75]

    K. Boshkayev, T. Konysbayev, Y. Kurmanov, O. Luongo, M. Muccino, A. Taukenova, and A. Urazalina, Luminosity of accretion disks around rotating regular black holes (2023), arXiv: 2307.15003 [gr-qc].

  • [76]

    Y. Kurmanov, K. Boshkayev, T. Konysbayev, O. Luongo, N. Saiyp, A. Urazalina, G. Ikhsan, and G. Suliyeva, Accretion disks properties around regular black hole solutions obtained from non-linear electrodynamics (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, T. Zhu, and B. Ahmedov, Physics of the Dark Universe 47, 101743 (2025)