Black holes immersed in modified Chaplygin-like dark fluid and cloud of strings: shadows, quasinomal modes and greybody factors

[1]
E. H. T. Collaboration, Astrophys. J. Lett. 875, L1 (2019)
[2]
E. H. T. Collaboration, Astrophys. J. Lett. 930, L12 (2022)
[3]
B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. Lett. 116, 061102 (2016)
[4]
V. Cardoso and P. Pani, Nature Astron. 1, 586 (2017), arXiv: 1709.01525[gr-qc]
[5]
V. Perlick and O. Y. Tsupko, Phys. Rept. 947, 1 (2022), arXiv: 2105.07101[gr-qc]
[6]
P. Kocherlakota and L. Rezzolla, Mon. Not. Roy. Astron. Soc. 513, 1229 (2022), arXiv: 2201.05641[gr-qc]
[7]
Y. Hou, Z. Zhang, H. Yan, M. Guo, and B. Chen, Phys. Rev. D 106, 064058 (2022), arXiv: 2206.13744[gr-qc]
[8]
Y. Hou, J. Huang, M. Guo, Y. Mizuno, and B. Chen, Astrophys. J. Lett. 988, L51 (2025), arXiv: 2409.07248[gr-qc]
[9]
M. Guo, N. A. Obers, and H. Yan, Phys. Rev. D 98, 084063 (2018), arXiv: 1806.05249[gr-qc]
[10]
P.-C. Li, M. Guo, and B. Chen, Phys. Rev. D 101, 084041 (2020a), arXiv: 2001.04231[gr-qc]
[11]
Z. Hu, Z. Zhong, P.-C. Li, M. Guo, and B. Chen, Phys. Rev. D 103, 044057 (2021), arXiv: 2012.07022[gr-qc]
[12]
Z. Zhao, Z.-Y. Fan, X. Wang, M. Guo, and B. Chen, Probing the Penrose Process: Images of Split Hotspots and Their Observational Signatures, (2025), arXiv: 2510.27409[astro-ph.HE]
[13]
Z.-Y. Fan, F. Zhou, Y. Li, M. Guo, and B. Chen, Phys. Rev. D 111, 064067 (2025), arXiv: 2411.19491[astro-ph.HE]
[14]
J.-Y. Gui, K.-J. He, H. Ye, and X.-X. Zeng, Front. Phys. (Beijing) 20, 25202 (2025), arXiv: 2407.09069[hep-th]
[15]
X.-X. Zeng, H.-Q. Zhang, and H. Zhang, Eur. Phys. J. C 80, 872 (2020), arXiv: 2004.12074[gr-qc]
[16]
X.-X. Zeng, G.-P. Li, and K.-J. He, Nucl. Phys. B 974, 115639 (2022), arXiv: 2106.14478[hep-th]
[17]
X.-X. Zeng, K.-J. He, J. Pu, G.-p. Li, and Q.-Q. Jiang, Eur. Phys. J. C 83, 897 (2023a), arXiv: 2302.03692[gr-qc]
[18]
K.-J. He, H. Ye, X.-X. Zeng, L.-F. Li, and P. Xu, Chin. Phys. 49, 125103 (2025a), arXiv: 2502.08388[gr-qc]
[19]
K.-J. He, G.-P. Li, C.-Y. Yang, and X.-X. Zeng, The observation image of a soliton boson star illuminated by various accretions, JCAP 10, 003, arXiv: 2502.16623[gr-qc]
[20]
X. Wang, Z. Zhao, X.-X. Zeng, and X.-Y. Wang, Phys. Rev. D 111, 084054 (2025), arXiv: 2501.08287[gr-qc]
[21]
E. Battista, Phys. Rev. D 109, 026004 (2024), arXiv: 2312.00450[gr-qc]
[22]
Z.-L. Wang and E. Battista, Eur. Phys. J. C 85, 304 (2025), arXiv: 2501.14516[gr-qc]
[23]
N. Tsukamoto, Z. Li, and C. Bambi, Constraining the spin and the deformation parameters from the black hole shadow, JCAP 06, 043, arXiv: 1403.0371[gr-qc]
[24]
N. Tsukamoto, Black hole shadow in an asymptotically-flat, stationary, Phys. Rev. D 97, 064021 (2018), arXiv: 1708.07427[gr-qc]
[25]
S.-b. Chen and J.-l. Jing, Class. Quant. Grav. 22, 4651 (2005), arXiv: gr-qc/0511085
[26]
R. A. Konoplya, Phys. Lett. B 795, 1 (2019), arXiv: 1905.00064[gr-qc]
[27]
X.-X. Zeng, H. Ye, K.-J. He, and H. Yu, Eur. Phys. J. C 85, 1211 (2025a), arXiv: 2507.11583[gr-qc]
[28]
X.-X. Zeng, M. I. Aslam, and R. Saleem, Eur. Phys. J. C 83, 129 (2023b), arXiv: 2208.06246[gr-qc]
[29]
X.-X. Zeng, C.-Y. Yang, M. I. Aslam, R. Saleem, and S. Aslam, Kerr-like black hole surrounded by cold dark matter halo: the shadow images and EHT constraints, JCAP 08, 066, arXiv: 2505.07063[gr-qc]
[30]
Y. Chen, R. Ding, Y. Liu, Y. Mizuno, J. Shu, H. Yu, and Y. Zeng, Phys. Rev. Lett. 135, 121001 (2025a), arXiv: 2404.16673[hep-ph]
[31]
E. Berti, V. Cardoso, and A. O. Starinets, Class. Quant. Grav. 26, 163001 (2009), arXiv: 0905.2975[gr-qc]
[32]
R. A. Konoplya and A. Zhidenko, Rev. Mod. Phys. 83, 793 (2011), arXiv: 1102.4014[gr-qc]
[33]
S. A. Teukolsky, Perturbations of a rotating black hole. I. Fundamental equations for gravitational, electromagnetic, Astrophys. J. 185, 635 (1973)
[34]
W. H. Press and S. A. Teukolsky, Astrophys. J. 185, 649 (1973)
[35]
H.-P. Nollert, Class. Quant. Grav. 16, R159 (1999)
[36]
C. Chen, J. Jing, Z. Cao, and M. Wang, Phys. Rev. D 112, 103036 (2025b), arXiv: 2506.14635[gr-qc]
[37]
Y. Guo, H. Xie, and Y.-G. Miao, Phys. Lett. B 855, 138801 (2024), arXiv: 2402.10406[gr-qc]
[38]
Y. Liu, B. Mu, J. Tao, and Y. Weng, Nucl. Phys. B 1010, 116787 (2025), arXiv: 2409.20333[gr-qc]
[39]
A. Zhidenko, Class. Quant. Grav. 21, 273 (2004), arXiv: gr-qc/0307012
[40]
S. W. Hawking, Commun. Math. Phys. 43, 199 (1975)
[41]
Y. Decanini, G. Esposito-Farese, and A. Folacci, Phys. Rev. D 83, 044032 (2011), arXiv: 1101.0781[gr-qc]
[42]
C.-Y. Zhang, P.-C. Li, and M. Guo, Eur. Phys. J. C 80, 874 (2020), arXiv: 2003.13068[hep-th]
[43]
V. Cardoso, A. S. Miranda, E. Berti, H. Witek, and V. T. Zanchin, Geodesic stability, Phys. Rev. D 79, 064016 (2009), arXiv: 0812.1806[hep-th]
[44]
H. Yang, D. A. Nichols, F. Zhang, A. Zimmerman, Z. Zhang, and Y. Chen, Phys. Rev. D 86, 104006 (2012), arXiv: 1207.4253[gr-qc]
[45]
K. Jusufi, Phys. Rev. D 101, 084055 (2020), arXiv: 1912.13320[gr-qc]
[46]
P.-C. Li, T.-C. Lee, M. Guo, and B. Chen, Phys. Rev. D 104, 084044 (2021), arXiv: 2105.14268[gr-qc]
[47]
J. A. V. Campos, M. A. Anacleto, F. A. Brito, and E. Passos, Sci. Rep. 12, 8516 (2022), arXiv: 2103.10659[hep-th]
[48]
R. A. Konoplya, A. Khrabustovskyi, J. Kříž, and A. Zhidenko, Quasinormal ringing and shadows of black holes and wormholes in dark matter-inspired Weyl gravity, JCAP 04, 062, arXiv: 2501.16134[gr-qc]
[49]
S.-H. Xiong, Y.-Z. Li, X.-M. Kuang, and J. Matyjasek, Eur. Phys. J. C 85, 1143 (2025), arXiv: 2508.03270[gr-qc]
[50]
N. Oshita, Phys. Rev. D 104, 124032 (2021), arXiv: 2109.09757[gr-qc]
[51]
R. F. Rosato, K. Destounis, and P. Pani, Phys. Rev. D 110, L121501 (2024), arXiv: 2406.01692[gr-qc]
[52]
N. Oshita, K. Takahashi, and S. Mukohyama, Phys. Rev. D 110, 084070 (2024), arXiv: 2406.04525[gr-qc]
[53]
R. A. Konoplya and A. Zhidenko, Correspondence between grey-body factors and quasinormal modes, JCAP 09, 068, arXiv: 2406.11694[gr-qc]
[54]
R. A. Konoplya, A. Zhidenko, and A. F. Zinhailo, Class. Quant. Grav. 36, 155002 (2019), arXiv: 1904.10333[gr-qc]
[55]
D. Pedrotti and M. Calzà, Trinity of black hole correspondences: Shadows, quasinormal modes, graybody factors, Phys. Rev. D 111, 124056 (2025), arXiv: 2504.01909[gr-qc]
[56]
Y. Guo, C. Lan, and Y.-G. Miao, Bounce corrections to gravitational lensing, quasinormal spectral stability, Phys. Rev. D 106, 124052 (2022), arXiv: 2201.02971[gr-qc]
[57]
Y. Guo and Y.-G. Miao, Charged black-bounce spacetimes: Photon rings, Nucl. Phys. B 983, 115938 (2022), arXiv: 2112.01747[gr-qc]
[58]
Y. Guo and Y.-G. Miao, Null geodesics, Phys. Rev. D 102, 084057 (2020), arXiv: 2007.08227[hep-th]
[59]
Q.-L. Shi, R. Wang, W. Xiong, and P.-C. Li, Quasinormal modes and grey-body factors of axial gravitational perturbations of regular black holes in asymptotically safe gravity, (2025), arXiv: 2506.16217[gr-qc]
[60]
A. G. Riess et al. (Supernova Search Team), Astron. J. 116, 1009 (1998), arXiv: astro-ph/9805201
[61]
S. Perlmutter et al. (Supernova Cosmology Project), Astrophys. J. 517, 565 (1999), arXiv: astro-ph/9812133
[62]
L.-M. Wang, R. R. Caldwell, J. P. Ostriker, and P. J. Steinhardt, Astrophys. J. 530, 17 (2000), arXiv: astro-ph/9901388
[63]
N. A. Bahcall, J. P. Ostriker, S. Perlmutter, and P. J. Steinhardt, Science 284, 1481 (1999), arXiv: astro-ph/9906463
[64]
V. V. Kiselev, Class. Quant. Grav. 20, 1187 (2003), arXiv: gr-qc/0210040
[65]
T. Lacroix and J. Silk, Astron. Astrophys. 554, A36 (2013), arXiv: 1211.4861[astro-ph.GA]
[66]
S. U. Khan and J. Ren, Phys. Dark Univ. 30, 100644 (2020), arXiv: 2006.11289[gr-qc]
[67]
X.-X. Zeng and H.-Q. Zhang, Eur. Phys. J. C 80, 1058 (2020), arXiv: 2007.06333[gr-qc]
[68]
A. He, J. Tao, Y. Xue, and L. Zhang, Chin. Phys. C 46, 065102 (2022), arXiv: 2109.13807[gr-qc]
[69]
D. J. Gogoi, N. Heidari, J. Kriz, and H. Hassanabadi, Fortsch. Phys. 72, 2300245 (2024), arXiv: 2307.09976[gr-qc]
[70]
G. Fatima, S. Shaukat, F. Javed, and G. Mustafa, Greybody factors, Phys. Dark Univ. 45, 101521 (2024)
[71]
B. Hamil and B. C. Lütfüo\uglu, Euler–Heisenberg Black Hole Surrounded by Quintessence in the Background of Perfect Fluid Dark Matter: Thermodynamics, Shadows, Fortsch. Phys. 73, 2400105 (2025a), arXiv: 2406.02109[gr-qc]
[72]
A. Kamenshchik, U. Moschella, and V. Pasquier, Phys. Lett. B 511, 265 (2001), arXiv: gr-qc/0103004[gr-qc]
[73]
N. Bilic, G. B. Tupper, and R. D. Viollier, Phys. Lett. B 535, 17 (2002), arXiv: astro-ph/0111325[astro-ph]
[74]
M. C. Bento, O. Bertolami, and A. A. Sen, Generalized Chaplygin gas, Phys. Rev. D 66, 043507 (2002), arXiv: gr-qc/0202064[gr-qc]
[75]
C.-G. Park, J.-c. Hwang, J. Park, and H. Noh, Phys. Rev. D 81, 063532 (2010), arXiv: 0910.4202[astro-ph.CO]
[76]
N. Aggarwal, A. Pourmand, F. Shojai, and H. Parthasarathy, Annals Phys. 483, 170266 (2025), arXiv: 2510.12472[gr-qc]
[77]
N. Ogawa, Phys. Rev. D 62, 085023 (2000), arXiv: hep-th/0003288
[78]
M. Bordemann and J. Hoppe, Phys. Lett. B 317, 315 (1993), arXiv: hep-th/9307036
[79]
R. Jackiw and A. P. Polychronakos, Phys. Rev. D 62, 085019 (2000), arXiv: hep-th/0004083
[80]
X.-Q. Li, B. Chen, and L.-l. Xing, Eur. Phys. J. Plus 135, 175 (2020b), arXiv: 1905.08156[gr-qc]
[81]
X.-Q. Li, B. Chen, and L.-L. Xing, Eur. Phys. J. Plus 137, 1167 (2022a), arXiv: 1908.09827[gr-qc]
[82]
X.-Q. Li, B. Chen, and L.-L. Xing, Annals Phys. 446, 169125 (2022b)
[83]
X.-Q. Li, H.-P. Yan, L.-L. Xing, and S.-W. Zhou, Phys. Rev. D 107, 104055 (2023), arXiv: 2305.03028[gr-qc]
[84]
X.-Q. Li, H.-P. Yan, X.-J. Yue, S.-W. Zhou, and Q. Xu, Geodesic structure, shadow and optical appearance of black hole immersed in Chaplygin-like dark fluid, JCAP 05, 048, arXiv: 2401.18066[gr-qc]
[85]
X.-Q. Li, Y. Kim, B.-H. Lee, H.-P. Yan, and X.-J. Yue, Black holes immersed in modified Chaplygin-like dark fluid and cloud of strings: geodesics, shadows, Chin. Phys. 49, 105104 (2025), arXiv: 2505.12077[gr-qc]
[86]
Y. Sekhmani, D. J. Gogoi, S. K. Maurya, K. Boshkayev, and M. K. Jasim, JHEAp 45, 200 (2025)
[87]
R. Bécar, P. A. González, E. Papantonopoulos, and Y. Vásquez, Massive scalar field perturbations of black holes immersed in Chaplygin-like dark fluid, JCAP 06, 061, arXiv: 2403.11306[gr-qc]
[88]
S. S. Bohra, Black hole perturbations in the Modified Generalized Chaplygin Gas model, (2025), arXiv: 2509.14064[gr-qc]
[89]
P. S. Letelier, Phys. Rev. D 20, 1294 (1979)
[90]
B. Hamil and B. C. Lütfüo\uglu, Chin. Phys. C 49, 025107 (2025b), arXiv: 2410.09551[gr-qc]
[91]
M. Sadeghi and H. Ranjbari, Class. Quant. Grav. 36, 205012 (2019), arXiv: 1905.12856[hep-th]
[92]
M. Sadeghi, Mod. Phys. Lett. A 35, 2050330 (2020), arXiv: 2001.01171[hep-th]
[93]
M. Sadeghi and F. Rahmani, Int. J. Mod. Phys. A 38, 2350102 (2023), arXiv: 2301.12411[hep-th]
[94]
M. Jaroszynski and A. Kurpiewski, Astron. Astrophys. 326, 419 (1997), arXiv: astro-ph/9705044
[95]
C. Bambi, Phys. Rev. D 87, 107501 (2013), arXiv: 1304.5691[gr-qc]
[96]
A. M. Bauer, A. Cárdenas-Avendaño, C. F. Gammie, and N. Yunes, Astrophys. J. 925, 119 (2022), arXiv: 2111.02178[gr-qc]
[97]
B. F. Schutz and C. M. Will, Astrophys. J. Lett. 291, L33 (1985)
[98]
S. Iyer and C. M. Will, Phys. Rev. D 35, 3621 (1987)
[99]
R. A. Konoplya, Phys. Rev. D 68, 024018 (2003), arXiv: gr-qc/0303052[gr-qc]
[100]
V. Ferrari and B. Mashhoon, Phys. Rev. D 30, 295 (1984)
[101]
B. Mashhoon, Phys. Rev. D 31, 290 (1985)