• [1]

    P. Gondolo and J. Silk, Phys. Rev. Lett. 83, 1719 (1999)

  • [2]

    M. Alloqulov, A. Abdujabbarov, B. Ahmedov et al., (2025), arXiv: 2512.12672[gr-qc]

  • [3]

    P. Ullio, H. Zhao, and M. Kamionkowski, Phys. Rev. D 64, 043504 (2001)

  • [4]

    I. R. King, Astrophys. J. 71, 64 (1966)

  • [5]

    P. H. Chavanis, M. Lemou, and F. Méhats, Phys. Rev. D 92, 123527 (2015), arXiv: 1409.7840[astro-ph.CO]

  • [6]

    N. Blinov, S. Profumo, and T. Stefaniak, JCAP 07, 028 (2015), arXiv: 1504.05949[hep-ph]

  • [7]

    S. N. Nuritdinov, A. A. Muminov, and F. U. Botirov, Astron. Astrophys. Trans. 32, 83 (2021), arXiv: 2002.09310[astro-ph.GA]

  • [8]

    A. Pathrikar, (2025), arXiv: 2511.02355[gr-qc]

  • [9]

    U. Uktamov, S. Shaymatov, B. Ahmedov et al., Eur. Phys. J. Plus 141, 513 (2026), arXiv: 2509.00460[gr-qc]

  • [10]

    F. Atamurotov, S. Shaymatov, P. Sheoran, and S. Siwach, JCAP 08, 045 (2021), arXiv: 2105.02214[gr-qc]

  • [11]

    G. Crisnejo, E. Gallo, and A. Rogers, Phys. Rev. D 99, 124001 (2019)

  • [12]

    F. Atamurotov, O. Yunusov, A. Abdujabbarov et al., New Astron. 105, 102098 (2024)

  • [13]

    K. Akiyama et al. (Event Horizon Telescope), Astrophys. J. Lett. 910, L13 (2021), arXiv: 2105.01173[astro-ph.HE]

  • [14]

    K. Akiyama et al. (Event Horizon Telescope), Astrophys. J. Lett. 930, L12 (2022), arXiv: 2311.08680[astro-ph.HE]

  • [15]

    F. Ahmed and E. O. Silva, (2025), arXiv: 2510.16260[gr-qc]

  • [16]

    S. Jumaniyozov, Eur. Phys. J. C 85, 1267 (2025)

  • [17]

    S. Zare, F. Hosseinifar, L. M. Nieto et al., (2025), arXiv: 2510.03925[gr-qc]

  • [18]

    U. Uktamov, S. Shaymatov, B. Ahmedov et al., Eur. Phys. J. C 85, 1432 (2025), arXiv: 2505.20031[gr-qc]

  • [19]

    J. Sharipov, T. Xamidov, Q. Wu et al., (2025), arXiv: 2511.10043[gr-qc]

  • [20]

    F. Atamurotov, A. Abdujabbarov, and J. Rayimbaev, Eur. Phys. J. C 81, 118 (2021)

  • [21]

    F. Mushtaq, X. Tiecheng, M. Yasir et al., Phys. Dark Univ. 50, 102109 (2025)

  • [22]

    S. Jumaniyozov, J. Rayimbaev, M. Akhmedov et al., Phys. Dark Univ. 50, 102161 (2025)

  • [23]

    M. Zahid, S. U. Khan, J. Ren et al., Int. J. Mod. Phys. D 31, 2250058 (2022)

  • [24]

    K. Kobialko, D. Gal’tsov, and A. Molchanov, Phys. Rev. D 112, 044039 (2025)

  • [25]

    S. Saydullayev, I. Nishonov, M. Dusaliyev et al., Eur. Phys. J. C 85, 1081 (2025)

  • [26]

    W. Javed, R. Babar, and A. Övgün, Phys. Rev. D 100, 104032 (2019), arXiv: 1910.11697[gr-qc]

  • [27]

    D. Umarov, F. Atamurotov, A. Abdujabbarov et al., (2026), arXiv: 2607.07487[gr-qc]

  • [28]

    S. Jumaniyozov, S. U. Khan, J. Rayimbaev et al., Phys. Rev. D 112, 044068 (2025)

  • [29]

    F. Ahmed, S. Shaymatov, C. Yuan et al., (2026), arXiv: 2607.24154[gr-qc]

  • [30]

    A. Ashraf, C. Yuan, A. Bouzenada et al., Int. J. Geom. Methods Mod. Phys. 23, 2650052 (2650)

  • [31]

    Z. Turakhonov, H. Hoshimov, A. Davlataliev et al., Nucl. Phys. B 1029, 117566 (2026)

  • [32]

    W. Yang, M. Alloqulov, A. Abdujabbarov et al., (2026), arXiv: 2603.15241[gr-qc]

  • [33]

    B. Shodikulov, M. Mirov, F. Atamurotov et al., Phys. Dark Univ. 50, 102096 (2025)

  • [34]

    S. Jumaniyozov, J. Rayimbaev, and Y. Turaev, Eur. Phys. J. C 85, 1247 (2025)

  • [35]

    P. Gibbon, in CAS - CERN Accelerator School 2019: High Gradient Wakefield Accelerators (2020), arXiv: 2007.04783[physics.acc-ph]

  • [36]

    M. Alloqulov, Y. Isaqjonov, S. Shaymatov et al., Chin. Phys. C 49, 045104 (2025)

  • [37]

    A. Alimova, Z. Turakhonov, F. Atamurotov et al., Phys. Dark Univ. 47, 101749 (2025)

  • [38]

    M. M. Gohain, K. Bhuyan, and P. Chutia, Phys. Dark Univ. 49, 102064 (2025), arXiv: 2504.00581[hep-th]

  • [39]

    F. Atamurotov, M. Jamil, and K. Jusufi, Chin. Phys. C 47, 035106 (2023), arXiv: 2212.12949[gr-qc]

  • [40]

    G. Mustafa, O. Donmez, D. J. Gogoi et al., JCAP 2026, 065 (2026), arXiv: 2602.08911[gr-qc]

  • [41]

    M. Zahid, J. Rayimbaev, F. Sarikulov et al., Eur. Phys. J. C 83, 855 (2023)

  • [42]

    J. Rayimbaev, D. Bardiev, T. Mirzaev et al., Int. J. Mod. Phys. D 31, 2250055 (2022)

  • [43]

    A. Chowdhuri and A. Bhattacharyya, Phys. Rev. D 104, 064039 (2021)

  • [44]

    M. Alloqulov, S. Shaymatov, A. Jawad et al., Commun. Theor. Phys. 77, 015402 (2025)

  • [45]

    A. Ashraf, O. Donmez, C. Yuan et al., Phys. Dark Univ. 52, 102274 (2026)

  • [46]

    M. A. Raza, J. Rayimbaev, F. Sarikulov et al., Phys. Dark Univ. 44, 101488 (2024)

  • [47]

    S. Kala and J. Singh, Eur. Phys. J. C 85, 1047 (2025), arXiv: 2507.17280[gr-qc]

  • [48]

    M. Alloqulov, F. Atamurotov, A. Abdujabbarov et al., Chin. Phys. C 48, 115116 (2024)

  • [49]

    S. Orzuev, F. Atamurotov, A. Abdujabbarov et al., New Astron. 105, 102104 (2024)

  • [50]

    M. Emtir, AJMAS 8(3), 1838 (2025)

  • [51]

    M. Yasir, F. Mushtaq, X. Tiecheng et al., Phys. Dark Univ. 48, 101838 (2025)

  • [52]

    G. Crisnejo and E. Gallo, Phys. Rev. D 97, 124016 (2018)

  • [53]

    W. Javed, I. Hussain, and A. Övgün, Eur. Phys. J. Plus 137, 148 (2022), arXiv: 2201.09879[gr-qc]

  • [54]

    Y. Feng, A. Ditta, G. Mustafa et al., Nucl. Phys. B 1008, 116713 (2024)

  • [55]

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

  • [56]

    G. Z. Babar, A. Z. Babar, and F. Atamurotov, Eur. Phys. J. C 80, 761 (2020) [Erratum: Eur. Phys. J. C 82, 403 (2022)], arXiv: 2008.05845[gr-qc]

  • [57]

    V. S. Morozova, B. J. Ahmedov, and A. A. Tursunov, Astrophys. Space Sci. 346, 513 (2013)

  • [58]

    A. Davlataliev, B. Narzilloev, I. Hussain et al., Phys. Dark Univ. 42, 101340 (2023)

  • [59]

    G. S. Bisnovatyi-Kogan and O. Y. Tsupko, Plasma Phys. Rep. 41, 562 (2015), arXiv: 1507.08545[gr-qc]

  • [60]

    Q. Li, Y. Zhang, Z. W. Lin et al., Mod. Phys. Lett. A 38, 2350025 (2023), arXiv: 2307.04444[grqc]

  • [61]

    H. Chakrabarty, A. B. Abdikamalov, A. A. Abdujabbarov et al., Phys. Rev. D 98, 024022 (2018), arXiv: 1804.00461[gr-qc]

  • [62]

    G. Z. Babar, F. Atamurotov, S. Ul Islam et al., Phys. Rev. D 103, 084057 (2021), arXiv: 2104.00714[gr-qc]

  • [63]

    G. Z. Babar, F. Atamurotov, and A. Z. Babar, Phys. Dark Univ. 32, 100798 (2021), arXiv: 2103.00316[gr-qc]

  • [64]

    C. A. Benavides-Gallego, A. A. Abdujabbarov, and C. Bambi, Eur. Phys. J. C 78, 694 (2018), arXiv: 1804.09434[gr-qc]

  • [65]

    D. Umarov, O. Yunusov, F. Atamurotov et al., Chin. Phys. C 49, 055102 (2025)