-
[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, Astrophys. Space Sci. 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 et al., Phys. Dark Univ. 46, 101566 (2024), arXiv: 2404.15437[gr-qc]
-
[6]
C. Lämmerzahl, M. Maceda, and A. Macías, Class. Quant. Grav. 36, 015001 (2019), arXiv: 1802.03766[gr-qc]
-
[7]
S. G. Ghosh and R. K. Walia, Ann. Phys. 434, 168619 (2021), arXiv: 2109.13031[gr-qc]
-
[8]
Planck Collaboration, A&A 641, A6 (2020), arXiv: 1807.06209[astro-ph.CO]
-
[9]
A. Das, A. Saha, and S. Gangopadhyay, Class. Quant. Grav. 38, 065015 (2021)
-
[10]
V. V. Kiselev, Class. Quant. Grav. 20, 1187 (2003), arXiv: gr-qc/0210040[gr-qc]
-
[11]
B. Toshmatov, Z. Stuchlík, and B. Ahmedov, Eur. Phys. J. Plus 132, 98 (2017)
-
[12]
F. Rahaman, K. K. Nandi, A. Bhadra et al., Phys. Lett. B 694, 10 (2010), arXiv: 1009.3572[gr-qc]
-
[13]
Y. Zhang and Y. X. Gui, Class. Quant. Grav. 23, 6141 (2006), arXiv: gr-qc/0612009[gr-qc]
-
[14]
S. G. Ghosh, S. D. Maharaj, D. Baboolal et al., Eur. Phys. J. C 78, 90 (2018), arXiv: 1708.03884[gr-qc]
-
[15]
S. U. Khan and J. Ren, Phys. Dark Univ. 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 et al., Phys. Rev. D 102, 104062 (2020), arXiv: 2011.06148[gr-qc]
-
[18]
S. U. Khan and J. Ren, Chin. J. Phys. 78, 141 (2022)
-
[19]
Mustafa, G. and Hussain, Ibrar, Eur. Phys. J. C 81, 419 (2021)
-
[20]
Mustafa, G. and Atamurotov, Farruh and Hussain et al., Chin. Phys. C 46, 125107 (2022), arXiv: 2207.07608[gr-qc]
-
[21]
I. Nishonov, J. Rayimbaev, S. U. Khan et al., Eur. Phys. J. C 85, 325 (2025)
-
[22]
M. Zahid, J. Rayimbaev, F. Sarikulov et al., Eur. Phys. J. C 83, 855 (2023)
-
[23]
S. U. Khan, J. Rayimbaev, F. Sarikulov et al., Chin. J. Phys. 90, 690 (2024), arXiv: 2310.05860[gr-qc]
-
[24]
M. H. Li and K. C. Yang, Phys. Rev. D 86, 123015 (2012), arXiv: 1204.3178[astro-ph.CO]
-
[25]
X. Hou, Z. Xu, and J. Wang, JCAP 2018, 040 (2018), arXiv: 1810.06381[gr-qc]
-
[26]
S. U. Khan, M. Shahzadi, and J. Ren, Phys. Dark Univ. 26, 100331 (2019), arXiv: 2005.09415[gr-qc]
-
[27]
R. A. Konoplya, Phys. Lett. B 795, 1 (2019), arXiv: 1905.00064[gr-qc]
-
[28]
S. Haroon, M. Jamil, K. Jusufi et al., Phys. Rev. D 99, 044015 (2019), arXiv: 1810.04103[gr-qc]
-
[29]
M. Akramov, B. Eshchanov, S. Usanov et al., Phys. Lett. A 524, 129827 (2024)
-
[30]
K. Jusufi, M. Jamil, and T. Zhu, Eur. Phys. J. C 80, 354 (2020), arXiv: 2005.05299[gr-qc]
-
[31]
J. Rayimbaev, S. Shaymatov, and M. Jamil, Eur. Phys. J. C 81, 699 (2021), arXiv: 2107.13436[gr-qc]
-
[32]
A. Kumar, A. Sood, J. K. Singh et al., Phys. Dark Univ. 40, 101220 (2023)
-
[33]
G. Rakhimova, F. Atamurotov, F. Javed et al., Nucl. Phys. B 996, 116363 (2023)
-
[34]
G. Mustafa, F. Javed, S. K. Maurya et al., Chin. J. Phys. 88, 32 (2024), arXiv: 2211.10778[gr-qc]
-
[35]
J. M. Bardeen, B. Carter, and S. W. Hawking, Commun. Math. Phys. 31, 161 (1973)
-
[36]
S. W. Hawking, Commun.Math. Phys. 43, 199 (1975)
-
[37]
S. W. Hawking, Phys. Rev. D 13, 191 (1976)
-
[38]
D. Kubizňák, R. B. Mann, and M. Teo, Class. Quant. Grav. 34, 063001 (2017), arXiv: 1608.06147[hep-th]
-
[39]
I. Kaygorodov, A. Khudoyberdiyev, and Z. Shermatova, J. Geom. Phys. 207, 105356 (2024), arXiv: 2406.15532 [math.RA]
-
[40]
B. Narzilloev and B. Ahmedov, New Astronomy 98, 101922 (2023)
-
[41]
M. Rizwan and K. Jusufi, Eur. Phys. J. C 83, 944 (2023), arXiv: 2310.15182[gr-qc]
-
[42]
A. A. Abdujabbarov, B. J. Ahmedov, and V. G. Kagramanova, Gen. Relativ. Gravit. 40, 2515 (2008), arXiv: 0802.4349[gr-qc]
-
[43]
V. P. Frolov, Phys. Rev. D 85, 024020 (2012), arXiv: 1110.6274[gr-qc]
-
[44]
J. Kovář, P. Slaný, C. Cremaschini et al., Phys. Rev. D 90, 044029 (2014), arXiv: 1409.0418[gr-qc]
-
[45]
A. Tursunov, Z. Stuchlík, and M. Kološ, Phys. Rev. D 93, 084012 (2016), arXiv: 1603.07264[gr-qc]
-
[46]
Z. Stuchlík and M. Kološ, Eur. Phys. J. C 76, 32 (2016), arXiv: 1511.02936[gr-qc]
-
[47]
M. Akramov, C. Trunk, J. Yusupov et al., Eur. Lett. 147, 62001 (2024), arXiv: 2411.14397[quant-ph]
-
[48]
J. Vrba, A. Abdujabbarov, A. Tursunov et al., Eur. Phys. J. C 79, 778 (2019), arXiv: 1909.12026[gr-qc]
-
[49]
J. Rayimbaev, M. Figueroa, Z. Stuchlík et al., Phys. Rev. D 101, 104045 (2020)
-
[50]
S. U. Khan and J. Ren, Chin. J. Phys. 70, 55 (2021), arXiv: 2010.02754[gr-qc]
-
[51]
M. Zahid, S. U. Khan, J. Ren et al., Int. J. Mod. Phys. D 31, 2250058 (2022)
-
[52]
S. U. Khan and Z.-M. Chen, Eur. Phys. J. C 83, 704 (2023)
-
[53]
B. Turimov, S. Usanov, and Y. Khamroev, (2025), arXiv: 2502.11185[gr-qc]
-
[54]
S. U. Khan, J. Ren, and J. Rayimbaev, Mod. Phys. Lett. A 37, 2250064 (2022)
-
[55]
S. U. Khan, U. Uktamov, J. Rayimbaev et al., Eur. Phys. J. C 84, 203 (2024)
-
[56]
B. Toshmatov, O. Rahimov, B. Ahmedov et al., Galaxies 9, 65 (2021)
-
[57]
B. Ahmedov, O. Rahimov, and B. Toshmatov, Universe 7, 307 (2021)
-
[58]
O. Rahimov, B. Toshmatov, Y. Vyblyi et al., Phys. Dark Univ. 44, 101483 (2024)
-
[59]
B. Turimov and O. Rahimov, Universe 8, 507 (2022)
-
[60]
B. Turimov, O. Rahimov, B. Ahmedov et al., Int. J. Mod. Phys. D 30, 2150037 (2021)
-
[61]
B. Turimov, A. Mamadjanov, and O. Rahimov, Galaxies 11, 70 (2023)
-
[62]
B. Rahmatov, M. Zahid, J. Rayimbaev et al., Chin. J. Phys. 92, 143 (2024)
-
[63]
Z. Hu, Z. Zhong, P. C. Li et al., Phys. Rev. D 103, 044057 (2021), arXiv: 2012.07022[gr-qc]
-
[64]
Z. Zhong, Z. Hu, H. Yan et al., Phys. Rev. D 104, 104028 (2021), arXiv: 2108.06140[gr-qc]
-
[65]
S. b. Yuan, C. k. Luo, Z. z. Hu et al., Chin. Phys. C 49, 025103 (2025), arXiv: 2403.06886[gr-qc]
-
[66]
M. Zhang and M. Guo, Eur. Phys. J. C 80, 790 (2020), arXiv: 1909.07033[gr-qc]
-
[67]
J. L. Synge, Mon. Not. Roy. Astron. Soc. 131, 463 (1966)
-
[68]
J. P. Luminet, A & A 75, 228 (1979)
-
[69]
J. M. Bardeen, Proceedings, Ecole d’Eté de Physique Théorique: Les Astres Occlus : Les Houches, France, August, 1972, 215-240, 215 (1973)
-
[70]
S. Chandrasekhar, The mathematical theory of black holes (1983)
-
[71]
A. de Vries, Class. Quant. Grav. 17, 123 (2000)
-
[72]
K. Hioki and K. i. Maeda, Phys. Rev. D 80, 024042 (2009)
-
[73]
A. A. Abdujabbarov, L. Rezzolla, and B. J. Ahmedov, Mon. Not. Roy. Astron. Soc. 454, 2423 (2015), arXiv: 1503.09054[gr-qc]
-
[74]
R. Takahashi, PASJ 57, 273 (2005), arXiv: astro-ph/0505316[astro-ph]
-
[75]
S. W. Wei and Y. X. Liu, JCAP 2013, 063 (2013), arXiv: 1311.4251[gr-qc]
-
[76]
A. Abdujabbarov, F. Atamurotov, Y. Kucukakca et al., Astrophys. Space Sci. 344, 429 (2013), arXiv: 1212.4949[physics.gen-ph]
-
[77]
L. Amarilla and E. F. Eiroa, Phys. Rev. D 85, 064019 (2012)
-
[78]
L. Amarilla and E. F. Eiroa, Phys. Rev. D 87, 044057 (2013)
-
[79]
F. Atamurotov, A. Abdujabbarov, and B. Ahmedov, Phys. Rev. D 88, 064004 (2013)
-
[80]
A. Grenzebach, V. Perlick, and C. Lämmerzahl, Phys. Rev. D 89, 124004 (2014), arXiv: 1403.5234[gr-qc]
-
[81]
U. Papnoi, F. Atamurotov, S. G. Ghosh et al., Phys. Rev. D 90, 024073 (2014), arXiv: 1407.0834[gr-qc]
-
[82]
P. V. P. Cunha, C. A. R. Herdeiro, E. Radu et al., Phys. Rev. Lett. 115, 211102 (2015), arXiv: 1509.00021[gr-qc]
-
[83]
Event Horizon Telescope Collaboration, ApJL 875, L5 (2019), arXiv: 1906.11242[astro-ph.GA]
-
[84]
The Event Horizon Telescope Collaboration, (2023), arXiv: 2311.08680[astro-ph.HE]
-
[85]
M. A. Raza, J. Rayimbaev, F. Sarikulov et al., Phys. Dark Univ. 44, 101488 (2024), arXiv: 2311.15784[gr-qc]
-
[86]
A. Abdujabbarov, B. Toshmatov, Z. Stuchlík et al., (2015), arXiv: 1512.05206[gr-qc]
-
[87]
C. Promsiri, W. Horinouchi, and E. Hirunsirisawat, (2024), arXiv: 2409.01582[gr-qc]
-
[88]
S. Guo, G. R. Li, and G. P. Li, Chin. Phys. C 46, 095101 (2022), arXiv: 2205.04957[gr-qc]
-
[89]
V. Vertogradov and A. Övgün, Class. Quant. Grav. 42, 025024 (2024)
-
[90]
K. A. Bronnikov, Phys. Rev. D 63, 044005 (2001)
-
[91]
C. Bambi, D. Malafarina, and L. Modesto, Phys. Rev. D 88, 044009 (2013)
-
[92]
E. Ayón-Beato and A. García, Phys. Rev. Lett. 80, 5056 (1998)
-
[93]
E. Ayon-Beato, Phys. Lett. B 464, 25 (1999)
-
[94]
E. Ayon-Beato and A. Garcia, Gen. Relativ. Gravit. 31, 629 (1999)
-
[95]
C. Bambi and L. Modesto, Phys. Lett. B 721, 329 (2013)
-
[96]
Z. Y. Fan and X. Wang, Phys. Rev. D 94, 124027 (2016)
-
[97]
J. S. B. Toshmatov, Z. Stuchlík, and B. Ahmedov, Phys. Rev. D 97, 084058 (2018)
-
[98]
Z. S. B. Toshmatov and B. Ahmedov, Phys. Rev. D 98, 085021 (2018)
-
[99]
O. Zaslavskii, Phys. Lett. B 688, 278 (2010)
-
[100]
J. Neves and A. Saa, Phys. Lett. B 734, 44 (2014)
-
[101]
S. Rakhmanov, K. Matchonov, H. Yusupov et al., Eur. Phys. J. B 98, 35 (2025)
-
[102]
E. A. Kontou and K. Sanders, Class. Quant. Grav. 37, 193001 (2020)
-
[103]
S. Capozziello, F. S. Lobo, and J. P. Mimoso, Phys. Lett. B 730, 280 (2014)
-
[104]
M. Novello, S. E. Perez Bergliaffa, and J. Salim, Phys. Rev. D 69, 127301 (2004)
-
[105]
R. Penrose, Phys. Rev. Lett. 14, 57 (1965)
-
[106]
V. Sahni and A. Starobinsky, Int. J. Mod. Phys. D 09, 373 (2000)
-
[107]
R. B. T. Ndongmo, S. Mahamat, T. B. Bouetou et al., Int. J. Theor. Phys. 63, 146 (2024)
-
[108]
B. Turimov, S. Usanov, and Y. Khamroev, Phys. Dark Univ. 48, 101876 (2025), arXiv: 2502.11185[gr-qc]
-
[109]
I. Dymnikova, Class. Quant. Grav. 21, 4417 (2004), arXiv: gr-qc/0407072[gr-qc]
-
[110]
Z. Stuchlík and J. Schee, Eur. Phys. J. C 79, 44 (2019)
-
[111]
J. Schee and Z. Stuchlík, Astrophys. J. 874, 12 (2019)
-
[112]
M. Zahid, F. Sarikulov, C. Shen et al., Phys. Dark Univ. 46, 101616 (2024)
-
[113]
M. Zubair, M. A. Raza, F. Sarikulov et al., JCAP 2023, 058 (2023), arXiv: 2305.16888[gr-qc]
-
[114]
D. J. Raine and E. G. Thomas, Black holes: an introduction (Imperial College Press, 2010)
-
[115]
S. Chandrasekhar, The mathematical theory of black holes, Vol. 69 (Oxford university press, 1998)
-
[116]
S. W. Wei and Y. X. Liu, Eur. Phys. J. Plus 136, 436 (2021)
-
[117]
M. Zahid, S. U. Khan, and J. Ren, Chin. J. Phys. 72, 575 (2021), arXiv: 2101.07673[gr-qc]
-
[118]
M. Zahid, F. Sarikulov, C. Shen et al., Chin. J. Phys. 91, 45 (2024)
-
[119]
M. Zahid, F. Sarikolov, S. Chao et al., Class. Quant. Grav. (2024).
-
[120]
S. Vagnozzi, R. Roy, Y. D. Tsai et al., (2022), arXiv: 2205.07787[gr-qc]
-
[121]
Y. Mizuno, Z. Younsi, C. M. Fromm et al., Nature Astron. 2, 585 (2018), arXiv: 1804.05812[astro-ph.GA]
-
[122]
P. Kocherlakota et al. (Event Horizon Telescope), Phys. Rev. D 103, 104047 (2021), arXiv: 2105.09343[gr-qc]
-
[123]
K. Akiyama et al. (Event Horizon Telescope), Astrophys. J. Lett. 875, L1 (2019), arXiv: 1906.11238[astroph.GA]
-
[124]
D. Wang, (2022), arXiv: 2205.08026[gr-qc]
-
[125]
K. Akiyama et al. (Event Horizon Telescope), Astrophys. J. Lett. 930, L12 (2022)
-
[126]
C. Bambi, K. Freese, S. Vagnozzi et al., Phys. Rev. D 100, 044057 (2019), arXiv: 1904.12983[gr-qc]