-
[1]
A. D. Sakharov, Soviet Journal of Experimental and Theoretical Physics 22, 241 (1966)
-
[2]
E. B. Gliner, Soviet Journal of Experimental and Theoretical Physics 22, 378 (1966)
-
[3]
L. E. Gurevich, Astrophysics and Space Science 38, 67 (1975)
-
[4]
A. A. Starobinskiǐ, Soviet Journal of Experimental and Theoretical Physics Letters 30, 682 (1979)
-
[5]
Y. Kurmanov, K. Boshkayev, T. Konysbayev, O. Luongo, N. Saiyp, A. Urazalina, G. Ikhsan, and G. Suliyeva, Physics of the Dark Universe 46, 101566 (2024), arXiv: 2404.15437[gr-qc]
-
[6]
C. Lämmerzahl, M. Maceda, and A. Macías, Classical and Quantum Gravity 36, 015001 (2019), arXiv: 1802.03766[gr-qc]
-
[7]
S. G. Ghosh and R. K. Walia, Annals of Physics 434, 168619 (2021), arXiv: 2109.13031[gr-qc]
-
[8]
Planck Collaboration, Astronomy and Astrophysics 641, A6 (2020), arXiv: 1807.06209[astro-ph.CO]
-
[9]
A. Das, A. Saha, and S. Gangopadhyay, Classical and Quantum Gravity 38, 065015 (2021)
-
[10]
V. V. Kiselev, Classical and Quantum Gravity 20, 1187 (2003), arXiv: gr-qc/0210040[gr-qc]
-
[11]
B. Toshmatov, Z. Stuchlík, and B. Ahmedov, European Physical Journal Plus 132, 98 (2017)
-
[12]
F. Rahaman, K. K. Nandi, A. Bhadra, M. Kalam, and K. Chakraborty, Physics Letters B 694, 10 (2010), arXiv: 1009.3572[gr-qc]
-
[13]
Y. Zhang and Y. X. Gui, Classical and Quantum Gravity 23, 6141 (2006), arXiv: gr-qc/0612009[gr-qc]
-
[14]
S. G. Ghosh, S. D. Maharaj, D. Baboolal, and T.-H. Lee, European Physical Journal C 78, 90 (2018), arXiv: 1708.03884[gr-qc]
-
[15]
S. U. Khan and J. Ren, Physics of the Dark Universe 30, 100644 (2020)
-
[16]
C. A. Benavides-Gallego, A. Abdujabbarov, and C. Bambi, Phys. Rev. D 101, 044038 (2020)
-
[17]
B. Narzilloev, J. Rayimbaev, S. Shaymatov, A. Abdujabbarov, B. Ahmedov, and C. Bambi, Phys. Rev. D 102, 104062 (2020), arXiv: 2011.06148[gr-qc]
-
[18]
S. U. Khan and J. Ren, Chinese Journal of Physics 78, 141 (2022)
-
[19]
Mustafa, G. and Hussain, Ibrar, European Physical Journal C 81, 419 (2021)
-
[20]
Mustafa, G. and Atamurotov, Farruh and Hussain, Ibrar and Shaymatov, Sanjar and Övgün, A li, Chinese Physics C 46, 125107 (2022), arXiv: 2207.07608[gr-qc]
-
[21]
M. Zahid, J. Rayimbaev, F. Sarikulov, S. U. Khan, and J. Ren, European Physical Journal C 83, 855 (2023)
-
[22]
S. U. Khan, J. Rayimbaev, F. Sarikulov, and O. Abdurakhmonov, Chinese Journal of Physics 90, 690 (2024), arXiv: 2310.05860[gr-qc]
-
[23]
M.-H. Li and K.-C. Yang, Phys. Rev. D 86, 123015 (2012), arXiv: 1204.3178[astro-ph.CO]
-
[24]
X. Hou, Z. Xu, and J. Wang, Journal of Cosmology and Astroparticle Physics 2018, 040 (2018), arXiv: 1810.06381[gr-qc]
-
[25]
S. U. Khan, M. Shahzadi, and J. Ren, Physics of the Dark Universe 26, 100331 (2019), arXiv: 2005.09415[gr-qc]
-
[26]
R. A. Konoplya, Physics Letters B 795, 1 (2019), arXiv: 1905.00064[gr-qc]
-
[27]
S. Haroon, M. Jamil, K. Jusufi, K. Lin, and R. B. Mann, Phys. Rev. D 99, 044015 (2019), arXiv: 1810.04103[gr-qc]
-
[28]
M. Akramov, B. Eshchanov, S. Usanov, S. Norbekov, and D. Matrasulov, Physics Letters A 524, 129827 (2024)
-
[29]
K. Jusufi, M. Jamil, and T. Zhu, European Physical Journal C 80, 354 (2020), arXiv: 2005.05299[gr-qc]
-
[30]
J. Rayimbaev, S. Shaymatov, and M. Jamil, European Physical Journal C 81, 699 (2021), arXiv: 2107.13436[gr-qc]
-
[31]
A. Kumar, A. Sood, J. K. Singh, A. Beesham, and S. G. Ghosh, Physics of the Dark Universe 40, 101220 (2023)
-
[32]
G. Rakhimova, F. Atamurotov, F. Javed, A. Abdujabbarov, and G. Mustafa, Nuclear Physics B 996, 116363 (2023)
-
[33]
Mustafa, G. and Javed, Faisal and Maurya, S. K. and Ray, Saibal, Chinese Journal of Physics 88, 32 (2024), arXiv: 2211.10778[gr-qc]
-
[34]
J. M. Bardeen, B. Carter, and S. W. Hawking, Communications in Mathematical Physics 31, 161 (1973)
-
[35]
S. W. Hawking, Communications in Mathematical Physics 43, 199 (1975)
-
[36]
S. W. Hawking, Phys. Rev. D 13, 191 (1976)
-
[37]
D. Kubizňák, R. B. Mann, and M. Teo, Classical and Quantum Gravity 34, 063001 (2017), arXiv: 1608.06147[hep-th]
-
[38]
I. Kaygorodov, A. Khudoyberdiyev, and Z. Shermatova, Journal of Geometry and Physics 207, 105356 (2025), arXiv: 2406.15532[math.RA]
-
[39]
B. Narzilloev and B. Ahmedov, 98 , 101922 (2023).
-
[40]
M. Rizwan and K. Jusufi, European Physical Journal C 83, 944 (2023), arXiv: 2310.15182[gr-qc]
-
[41]
A. A. Abdujabbarov, B. J. Ahmedov, and V. G. Kagramanova, General Relativity and Gravitation 40, 2515 (2008), arXiv: 0802.4349[gr-qc]
-
[42]
V. P. Frolov, Phys. Rev. D 85, 024020 (2012), arXiv: 1110.6274[gr-qc]
-
[43]
J. Kovář, P. Slaný, C. Cremaschini, Z. Stuchlík, V. Karas, and A. Trova, Phys. Rev. D 90, 044029 (2014), arXiv: 1409.0418[gr-qc]
-
[44]
A. Tursunov, Z. Stuchlík, and M. Kološ, Phys. Rev. D 93, 084012 (2016), arXiv: 1603.07264[gr-qc]
-
[45]
Z. Stuchlík and M. Kološ, European Physical Journal C 76, 32 (2016), arXiv: 1511.02936[gr-qc]
-
[46]
M. Akramov, C. Trunk, J. Yusupov, and D. Matrasulov, EPL (Europhysics Letters) 147, 62001 (2024), arXiv: 2411.14397[quant-ph]
-
[47]
J. Vrba, A. Abdujabbarov, A. Tursunov, B. Ahmedov, and Z. Stuchlík, European Physical Journal C 79, 778 (2019), arXiv: 1909.12026[gr-qc]
-
[48]
J. Rayimbaev, M. Figueroa, Z. Stuchlík, and B. Juraev, Phys. Rev. D 101, 104045 (2020)
-
[49]
S. U. Khan and J. Ren, Chinese Journal of Physics 70, 55 (2021), arXiv: 2010.02754[gr-qc]
-
[50]
J. Rayimbaev, S. Shaymatov, and M. Jamil, European Physical Journal C 81, 699 (2021), arXiv: 2107.13436[gr-qc]
-
[51]
M. Zahid, S. U. Khan, J. Ren, and J. Rayimbaev, International Journal of Modern Physics D 31, 2250058 (2022)
-
[52]
S. U. Khan and Z.-M. Chen, European Physical Journal C 83, 704 (2023)
-
[53]
B. Turimov, S. Usanov, and Y. Khamroev, arXiv eprints, arXiv: 2502.11185 (2025), arXiv: 2502.11185[gr-qc].
-
[54]
S. U. Khan, J. Ren, and J. Rayimbaev, Modern Physics Letters A 37, 2250064 (2022)
-
[55]
S. U. Khan, U. Uktamov, J. Rayimbaev, A. Abdujabbarov, I. Ibragimov, and Z.-M. Chen, European Physical Journal C 84, 203 (2024)
-
[56]
S. U. Khan, J. Rayimbaev, F. Sarikulov, and O. Abdurakhmonov, Chinese Journal of Physics 90, 690 (2024), arXiv: 2310.05860[gr-qc]
-
[57]
B. Toshmatov, O. Rahimov, B. Ahmedov, and A. Ahmedov, Galaxies 9, 65 (2021)
-
[58]
B. Ahmedov, O. Rahimov, and B. Toshmatov, Universe 7, 307 (2021)
-
[59]
O. Rahimov, B. Toshmatov, Y. Vyblyi, A. Akhmedov, and B. Abdulazizov, Physics of the Dark Universe 44, 101483 (2024)
-
[60]
B. Turimov and O. Rahimov, Universe 8, 507 (2022)
-
[61]
B. Turimov, O. Rahimov, B. Ahmedov, Z. Stuchlík, and K. Boymurodova, International Journal of Modern Physics D 30, 2150037 (2021)
-
[62]
B. Turimov, A. Mamadjanov, and O. Rahimov, Galaxies 11, 70 (2023)
-
[63]
B. Rahmatov, M. Zahid, J. Rayimbaev, R. Rahim, and S. Murodov, Chin. J. Phys. 92, 143 (2024)
-
[64]
Z. Hu, Z. Zhong, P.-C. Li, M. Guo, and B. Chen, Phys. Rev. D 103, 044057 (2021), arXiv: 2012.07022[gr-qc]
-
[65]
Z. Zhong, Z. Hu, H. Yan, M. Guo, and B. Chen, Phys. Rev. D 104, 104028 (2021), arXiv: 2108.06140[gr-qc]
-
[66]
S.-b. Yuan, C.-k. Luo, Z.-z. Hu, Z.-y. Zhang, and B. Chen, Chinese Physics C 49, 025103 (2025), arXiv: 2403.06886[gr-qc]
-
[67]
M. Zhang and M. Guo, European Physical Journal C 80, 790 (2020), arXiv: 1909.07033[gr-qc]
-
[68]
J. L. Synge, Mon. Not. Roy. Astron. Soc. 131, 463 (1966)
-
[69]
J. P. Luminet, Astronomy and Astrophysics 75, 228 (1979)
-
[70]
J. M. Bardeen, Proceedings, Ecole d’Eté de Physique Théorique: Les Astres Occlus : Les Houches, France, August, 1972, 215-240, 215 (1973).
-
[71]
S. Chandrasekhar, The mathematical theory of black holes (1983).
-
[72]
A. de Vries, Classical and Quantum Gravity 17, 123 (2000)
-
[73]
K. Hioki and K.-i. Maeda, Phys. Rev. D 80, 024042 (2009)
-
[74]
A. A. Abdujabbarov, L. Rezzolla, and B. J. Ahmedov, Monthly Notices of the Royal Astronomical Society 454, 2423 (2015), arXiv: 1503.09054[gr-qc]
-
[75]
R. Takahashi, Publications of the Astronomical Society of Japan 57, 273 (2005), arXiv: astro-ph/0505316[astro-ph]
-
[76]
S.-W. Wei and Y.-X. Liu, Journal of Cosmology and Astroparticle Physics 2013, 063 (2013), arXiv: 1311.4251[gr-qc]
-
[77]
A. Abdujabbarov, F. Atamurotov, Y. Kucukakca, B. Ahmedov, and U. Camci, Astrophysics and Space Science 344, 429 (2013), arXiv: 1212.4949[physics.gen-ph]
-
[78]
L. Amarilla and E. F. Eiroa, Phys. Rev. D 85, 064019 (2012)
-
[79]
L. Amarilla and E. F. Eiroa, Phys. Rev. D 87, 044057 (2013)
-
[80]
F. Atamurotov, A. Abdujabbarov, and B. Ahmedov, Phys. Rev. D 88, 064004 (2013)
-
[81]
A. Grenzebach, V. Perlick, and C. Lämmerzahl, Phys. Rev. D 89, 124004 (2014), arXiv: 1403.5234[gr-qc]
-
[82]
U. Papnoi, F. Atamurotov, S. G. Ghosh, and B. Ahmedov, Phys. Rev. D 90, 024073 (2014), arXiv: 1407.0834[gr-qc]
-
[83]
P. V. P. Cunha, C. A. R. Herdeiro, E. Radu, and H. F. Runarsson, Phys. Rev. Lett. 115, 211102 (2015), arXiv: 1509.00021[gr-qc]
-
[84]
Event Horizon Telescope Collaboration, Astrophysical Journal Letters 875, L5 (2019), arXiv: 1906.11242[astro-ph.GA]
-
[85]
The Event Horizon Telescope Collaboration, arXiv e-prints, arXiv: 2311.08680 (2023), arXiv: 2311.08680[astro-ph.HE].
-
[86]
M. A. Raza, J. Rayimbaev, F. Sarikulov, M. Zubair, B. Ahmedov, and Z. Stuchlík, Physics of the Dark Universe 44, 101488 (2024), arXiv: 2311.15784[gr-qc]
-
[87]
A. Abdujabbarov, B. Toshmatov, Z. Stuchlík, and B. Ahmedov, arXiv e-prints, arXiv: 1512.05206 (2015), arXiv: 1512.05206[gr-qc].
-
[88]
C. Promsiri, W. Horinouchi, and E. Hirunsirisawat, arXiv e-prints, arXiv: 2409.01582 (2024), arXiv: 2409.01582[gr-qc].
-
[89]
S. Guo, G.-R. Li, and G.-P. Li, Chinese Physics C 46, 095101 (2022), arXiv: 2205.04957[gr-qc]
-
[90]
V. Vertogradov and A. Övgün, Classical and Quantum Gravity 42, 025024 (2024)
-
[91]
K. A. Bronnikov, Physical Review D 63, 044005 (2001)
-
[92]
C. Bambi, D. Malafarina, and L. Modesto, Physical Review D 88 (2013), 10.1103/physrevd.88.044009.
-
[93]
E. Ayón-Beato and A. García, Physical Review Letters 80, 5056 (1998)
-
[94]
E. Ayon-Beato, Physics Letters B 464, 25 (1999)
-
[95]
E. Ayon-Beato and A. Garcia, General Relativity and Gravitation 31, 629 (1999)
-
[96]
C. Bambi and L. Modesto, Physics Letters B 721, 329 (2013)
-
[97]
J. Rayimbaev, M. Figueroa, Z. c. v. Stuchlík, and B. Juraev, Phys. Rev. D 101, 104045 (2020)
-
[98]
Z.-Y. Fan and X. Wang, Physical Review D 94, 124027 (2016)
-
[99]
J. S. B. Toshmatov, Z. Stuchlík and B. Ahmedov, Physical Review D 97, 084058 (2018)
-
[100]
Z. S. B. Toshmatov and B. Ahmedov, Physical Review D 98, 085021 (2018)
-
[101]
Z.-Y. Fan and X. Wang, Physical Review D 94 (2016), 10.1103/physrevd.94.124027.
-
[102]
O. Zaslavskii, Physics Letters B 688, 278 (2010)
-
[103]
J. Neves and A. Saa, Physics Letters B 734, 44 (2014)
-
[104]
S. Rakhmanov, K. Matchonov, H. Yusupov, K. Nasriddinov, and D. Matrasulov, The European Physical Journal B 98, 35 (2025)
-
[105]
E.-A. Kontou and K. Sanders, Classical and Quantum Gravity 37, 193001 (2020)
-
[106]
S. Capozziello, F. S. Lobo, and J. P. Mimoso, Physics Letters B 730, 280 (2014)
-
[107]
M. Novello, S. E. Perez Bergliaffa, and J. Salim, Physical Review D 69 (2004), 10.1103/physrevd.69.127301.
-
[108]
J. M. Bardeen, B. Carter, and S. W. Hawking, Commun. Math. Phys. 31, 161 (1973)
-
[109]
R. Penrose, Phys. Rev. Lett. 14, 57 (1965)
-
[110]
V. SAHNI and A. STAROBINSKY, International Journal of Modern Physics D 09, 373 (2000)
-
[111]
R. B. T. Ndongmo, S. Mahamat, T. B. Bouetou, C. B. Tabi, and T. C. Kofane, International Journal of Theoretical Physics 63 (2024), 10.1007/s10773-024-05687-8.
-
[112]
B. Turimov, S. Usanov, and Y. Khamroev, Physics of the Dark Universe 48, 101876 (2025), arXiv: 2502.11185[gr-qc]
-
[113]
I. Dymnikova, Classical and Quantum Gravity 21, 4417 (2004), arXiv: gr-qc/0407072[gr-qc]
-
[114]
Z. Stuchlík and J. Schee, European Physical Journal C 79, 44 (2019)
-
[115]
J. Schee and Z. Stuchlík, The Astrophysical Journal 874, 12 (2019)
-
[116]
M. Zahid, F. Sarikulov, C. Shen, M. Umaraliyev, and J. Rayimbaev, Physics of the Dark Universe 46, 101616 (2024)
-
[117]
M. Zubair, M. A. Raza, F. Sarikulov, and J. Rayimbaev, Journal of Cosmology and Astroparticle Physics 2023, 058 (2023), arXiv: 2305.16888[gr-qc]
-
[118]
D. J. Raine and E. G. Thomas, Black holes: an introduction (Imperial College Press, 2010).
-
[119]
S. Chandrasekhar, The mathematical theory of black holes, Vol. 69 (Oxford university press, 1998).
-
[120]
S.-W. Wei and Y.-X. Liu, The European Physical Journal Plus 136, 436 (2021)
-
[121]
U. Papnoi, F. Atamurotov, S. G. Ghosh, and B. Ahmedov, Physical Review D 90, 024073 (2014)
-
[122]
M. Zahid, S. U. Khan, and J. Ren, Chinese Journal of Physics 72, 575 (2021), arXiv: 2101.07673[gr-qc]
-
[123]
M. Zahid, F. Sarikulov, C. Shen, M. Umaraliyev, and J. Rayimbaev, Phys. Dark Univ. 46, 101616 (2024)
-
[124]
M. Zahid, F. Sarikulov, C. Shen, J. Rayimbaev, K. Badalov, and S. Muminov, Chin. J. Phys. 91, 45 (2024)
-
[125]
M. Zahid, F. Sarikolov, S. Chao, J. Rayimbaev, and S. Ahmedov, Classical and Quantum Gravity (2024).
-
[126]
S. Vagnozzi, R. Roy, Y.-D. Tsai, and L. Visinelli, (2022), arXiv: 2205.07787[gr-qc].
-
[127]
Y. Mizuno, Z. Younsi, C. M. Fromm, O. Porth, M. De Laurentis, H. Olivares, H. Falcke, M. Kramer, and L. Rezzolla, Nature Astron. 2, 585 (2018), arXiv: 1804.05812[astro-ph.GA]
-
[128]
P. Kocherlakota et al. (Event Horizon Telescope), Phys. Rev. D 103, 104047 (2021), arXiv: 2105.09343[gr-qc]
-
[129]
K. Akiyama et al. (Event Horizon Telescope), Astrophys. J. Lett. 875, L1 (2019), arXiv: 1906.11238[astroph.GA]
-
[130]
D. Wang, (2022), arXiv: 2205.08026[gr-qc].
-
[131]
K. Akiyama et al. (Event Horizon Telescope), Astrophys. J. Lett. 930, L12 (2022)
-
[132]
C. Bambi, K. Freese, S. Vagnozzi, and L. Visinelli, Phys. Rev. D 100, 044057 (2019), arXiv: 1904.12983[gr-qc]