- 
								[1]
								R. Penrose, Phys. Rev. Lett. 14, 57 (1965) 
- 
								[2]
								B. P. Abbott et al., Phys. Rev. Lett. 116, 061102 (2016) 
- 
								[3]
								K. Akiyama, et al., ApJL 875(1), L6 (2019) 
- 
								[4]
								K. Akiyama, et al., ApJL 930(2), L14 (2022) 
- 
								[5]
								S. Gillessen, F. Eisenhauer, S. Trippe et al., ApJ 692(2), 1075 (2009) 
- 
								[6]
								R. Abuter et al., A&A 625, L10 (2019) 
- 
								[7]
								M. D. Laurentis, I. de Martino, and R. D. Monica, Rep. Prog. Phys. 86(10), 104901 (2023) 
- 
								[8]
								R. D. Monica and I. de Martino, JCAP 2022(03), 007 (2022) 
- 
								[9]
								R. Abuter et al., A&A 636, L5 (2020) 
- 
								[10]
								R. Abuter et al., A&A 615, L15 (2018) 
- 
								[11]
								R. Della Monica and I. de Martino, Phys. Rev. D 108, L101303 (2023) 
- 
								[12]
								A. Foschi et al., MNRAS 524(1), 1075 (2023) 
- 
								[13]
								A. Foschi et al., MNRAS 530(4), 3740 (2024) 
- 
								[14]
								R. Della Monica, I. de Martino, and M. de Laurentis, MNRAS 510(4), 4757 (2021) 
- 
								[15]
								J. M. Yan, Q. Wu, C. Liu et al., JCAP 2022(09), 008 (2022) 
- 
								[16]
								X. Li, X. Zhang, and H. N. Lin, Phys. Rev. D 106, 064043 (2022) 
- 
								[17]
								J. M. Yan, C. Liu, T. Zhu et al., Phys. Rev. D 107, 084043 (2023) 
- 
								[18]
								Z. Zhang, S. Chen, and J. Jing, Eur. Phys. J. C 84(8), 827 (2024) 
- 
								[19]
								I. De Martino, R. Della Monica, and D. Rubiera-Garcia, Phys. Rev. D 109, 024016 (2024) 
- 
								[20]
								Y. Tan and Y. Lu, Phys. Rev. D 109, 044047 (2024) 
- 
								[21]
								R. Genzel, R. Schödel, T. Ott et al., Nature 425, 934 (2003) 
- 
								[22]
								B. Aschenbach, N. Grosso, D. Porquet et al., A&A 417(1), 71 (2004) 
- 
								[23]
								B. Aschenbach, A&A 425(3), 1075 (2004) 
- 
								[24]
								M. Zubair, M. A. Raza, and G. Abbas, Eur. Phys. J. C 82(10), 948 (2022) 
- 
								[25]
								M. Zubair, M. A. Raza, and E. Maqsood, Phys. Dark Univ. 42, 101334 (2023) 
- 
								[26]
								M. Zubair, M. A. Raza, F. Sarikulov et al., JCAP 2023(10), 058 (2023) 
- 
								[27]
								M. A. Raza, J. Rayimbaev, F. Sarikulov et al., Phys. Dark Univ. 44, 101488 (2024) 
- 
								[28]
								M. A. Raza, M. Zubair, and E. Maqsood, JCAP 2024(05), 047 (2024) 
- 
								[29]
								A. G. Riess et al., Astroph. J. 116(3), 1009 (1998) 
- 
								[30]
								S. Perlmutter et al., Astroph. J. 517(2), 565 (1999) 
- 
								[31]
								V. Balasubramanian, J. de Boer, and D. Minic, Phys. Rev. D 65, 123508 (2002) 
- 
								[32]
								M. Cvetič, H. Lü, and C. Pope, Phys. Lett. B 598(3), 273 (2004) 
- 
								[33]
								B. P. Dolan, D. Kastor, D. Kubizňák et al., Phys. Rev. D 87, 104017 (2013) 
- 
								[34]
								D. Castelvecchi, Nature (2016) 
- 
								[35]
								P. J. E. Peebles and B. Ratra, Rev. Mod. Phys. 75, 559 (2003) 
- 
								[36]
								P. C. Li, M. Guo, and B. Chen, Phys. Rev. D 101, 084041 (2020) 
- 
								[37]
								E. Omwoyo, H. Belich, J. C. Fabris et al., Eur. Phys. J. Plus 138, 1043 (2023) 
- 
								[38]
								Q.-H. Zhu, Phys. Rev. D 109, 044057 (2024) 
- 
								[39]
								G. V. Kraniotis, Class. Quantum Grav. 21(19), 4743 (2004) 
- 
								[40]
								G. V. Kraniotis, Class. Quantum Grav. 24(7), 1775 (2007) 
- 
								[41]
								S. Gillessen et al., Astroph. J. 837(1), 30 (2017) 
- 
								[42]
								B. Carter, Commun. Math. Phys. 10(4), 280 (1968) 
- 
								[43]
								S. Bhattacharya, Phys. Rev. D 97, 084049 (2018) 
- 
								[44]
								S. Akcay and R. A. Matzner, Class. Quantum Grav. 28(8), 085012 (2011) 
- 
								[45]
								J. B. Griffiths, J. Podolský,Cambridge Monographs on Mathematical Physics, (Cambridge University Press, 2009) 
- 
								[46]
								P. Hintz and A. Vasy, Commun. Math. Phys. 58(8), 081509 (2017) 
- 
								[47]
								D. Charbulák and Z. Stuchlík, Eur. Phys. J. C 77(12), 897 (2017) 
- 
								[48]
								S. G. Ghosh, M. Amir, and S. D. Maharaj, Nucl. Phys. B 957, 115088 (2020) 
- 
								[49]
								R. Penrose and R. M. Floyd, Nature Physical Science 229, 177 (1971) 
- 
								[50]
								B. Carter, Phys. Rev. 174, 1559 (1968) 
- 
								[51]
								J. Lense and H. Thirring, Phys. Z. 19, 156 (1918) 
- 
								[52]
								A. Stepanian, S. Khlghatyan, and V. Gurzadyan, Eur. Phys. J. C 80(11), 1011 (2020) 
- 
								[53]
								A. Stepanian and S. Khlghatyan, Eur. Phys. J. C Plus 135(9), 712 (2020) 
- 
								[54]
								F. Zhang, Y. Lu, and Q. Yu, Astroph. J. 809(2), 127 (2015) 
- 
								[55]
								T. Alexander, Phys. Rep. 419 (2), 65 (2005) 
- 
								[56]
								S. M. Carroll, Spacetime and Geometry: An Introduction to General Relativity, (Cambridge University Press, 2019) 
- 
								[57]
								M. Grould, F. H. Vincent, T. Paumard et al., A&A 608, A60 (2017) 
- 
								[58]
								T. Do et al., Science 365(6454), 664 (2019) 
- 
								[59]
								D. Foreman-Mackey, D. W. Hogg, D. Lang, J. Goodman, PASP 125(925), 306 (2013) 
- 
								[60]
								I. Waisberg, J. Dexter, S. Gillessen et al., MNRAS 476(3), 3600 (2018) 
- 
								[61]
								M. Sereno and P. Jetzer, Phys. Rev. D 73, 063004 (2006)