- 
								[1]
								T. Jacobson, Phys. Rev. Lett. 75, 1260 (1995) 
- 
								[2]
								T. Padmanabhan, Rept. Prog. Phys. 73, 046901 (2010) 
- 
								[3]
								J. D. Bekenstein, Phys. Rev. D 7, 2333 (1973) 
- 
								[4]
								S. W. Hawking, Commun. Math. Phys. 43, 199 (1975) 
- 
								[5]
								S. W. Hawking and Don N. Page, Commun. Math. Phys. 87, 577 (1983) 
- 
								[6]
								J. M. Maldacena, Adv. Theor. Math. Phys. 2, 231 (1998) 
- 
								[7]
								E. Witten, Adv. Theor. Math. Phys. 2, 505 (1998), arXiv: hep-th/9803131 
- 
								[8]
								A. Chamblin, R. Emparan, C. V. Johnson et al., Phys. Rev. D 60, 064018 (1999), arXiv: hep-th/9902170 
- 
								[9]
								D. Kastor, S. Ray, and J. Traschen, Class. Quantum Grav. 26, 195011 (2009) 
- 
								[10]
								D. Kubiznak and R. B. Mann, J. High Energ. Phys. 2012(07), 033 (2012), arXiv: 1205.0559 
- 
								[11]
								S. W Wei and Y. X Liu, Phys. Rev. Lett. 115, 111302 (2015) 
- 
								[12]
								S. W Wei and Y. X Liu, Sci. China Phys. Mech. Astron. 67(5), 250412 (2024) 
- 
								[13]
								N. Altamirano, D. Kubiznak and R. B. Mann, Phys. Rev. D 88, 101502 (2013), arXiv: 1306.5756 
- 
								[14]
								A. M. Frassino, D. Kubiznak, R. B. Mann et al., J. High Energ. Phys. 2014(09), 080 (2014), arXiv: 1406.7015 
- 
								[15]
								R. A. Hennigar and R. B. Mann, Phys. Rev. Lett. 118, 021301 (2017), arXiv: 1609.02564 
- 
								[16]
								B. P. Dolan, A. Kostouki, D. Kubiznak et al., Class. Quantum Grav. 31, 242001 (2014) 
- 
								[17]
								S. W Wei and Y. X Liu, Phys. Rev. D 90, 044057 (2014) 
- 
								[18]
								M. D Li, H. M Wang, and S. W Wei, Phys. Rev. D 105, 104013 (2022) 
- 
								[19]
								S. W Wei, Y. X Liu, and R. B. Man, Phys. Rev. D 102, 104011 (2020) 
- 
								[20]
								S. W Wei, Y. X Liu, and R. B. Man, Phys. Rev. D 110, L081501 (2024) 
- 
								[21]
								S. W Wei, Y. X Liu, and R. B. Man, Phys. Rev. Lett. 129, 191101 (2022) 
- 
								[22]
								R. G Cai, L. M Cao, L. Li et al., J. High Energ. Phys. 2013(09), 005 (2013), arXiv: 1306.6233 
- 
								[23]
								C. V. Johnson, Class. Quantum Grav. 31, 205002 (2014) 
- 
								[24]
								H. Xu, Y. Sun, and L. Zhao, Int. J. Mod. Phys. D 26, 13 (2017) 
- 
								[25]
								D. Kubiznak, R. B. Mann, and M. Teo, Class. Quantum Grav. 34, 063001 (2017) 
- 
								[26]
								J. L Zhang, R. G Cai, and H. Yu, Phys. Rev. D 91, 044028 (2015) 
- 
								[27]
								B. P. Dolan, Entropy 18, 169 (2016) 
- 
								[28]
								B. P. Dolan, J. High Energ. Phys. 2014(10), 179 (2014) 
- 
								[29]
								D. Kastor, S. Ray, and J. Traschen, J. High Energ. Phys. 2014(11), 120 (2014) 
- 
								[30]
								A. Karch and B. Robinson, J. High Energ. Phys. 2015(12), 073 (2015) 
- 
								[31]
								M. Sinamuli and R. B Mann, Phys. Rev. D 96, 086008 (2017) 
- 
								[32]
								W. Cong, D. Kubiznak, and R. B Mann, Phys. Rev. Lett. 127, 091301 (2021) 
- 
								[33]
								M. R. Visser, Phys. Rev. D 105, 106014 (2022) 
- 
								[34]
								Z. Gao and L. Zhao, Class. Quantum Grav. 39, 7 (2022) 
- 
								[35]
								L. Zhao, Chin. Phys. C 46, 055105 (2022) 
- 
								[36]
								J. Sadeghi, M. Shokri, S. N. Gashti et al., Gen. Relativ. Gravit. 54, 129 (2022), arXiv: 2205.03648 
- 
								[37]
								M. Zhang, Z. Y. Yang, D. C. Zou et al., Gen. Relativ. Gravit. 47, 14 (2015), arXiv: 1412.1197 
- 
								[38]
								C. Corda and H. J. Mosquera Cuesta, Astropart. Phys. 34, 587 (2011), arXiv: 1011.4801[physics.gen-ph] 
- 
								[39]
								S. H. Mazharimousavi and M. Halilsoy, Phys. Lett. B 681, 190 (2009), arXiv: 0908.0308 
- 
								[40]
								V. A. De Lorenci, R. Klippert, M. Novello et al., Phys. Rev. D 65, 063501 (2002) 
- 
								[41]
								N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Spacetime, (Cambridge: Cambridge University Press, 1982) 
- 
								[42]
								E. M. C. Abreu and J. A. Neto, Phys. Lett. B 810, 135805 (2020) 
- 
								[43]
								J. D. Barrow, Phys. Lett. B 808, 135643 (2020) 
- 
								[44]
								E. N. Saridakis, Phys. Rev. D 102, 123525 (2020) 
- 
								[45]
								H. Moradpour, A. H. Ziaie, and M. Kord Zangeneh, Eur. Phys. J. C 80, 732 (2020) 
- 
								[46]
								A. Salehi, Eur. Phys. J. C 83, 11 (2023) 
- 
								[47]
								N. Komatsu, Phys. Rev. D 109, 023505 (2024) 
- 
								[48]
								O. Okcu, Nucl. Phys. B 1004, 116551 (2024) 
- 
								[49]
								E. M. C. Abreu, J. A. Neto, and E. M. Barboza, Europhys. Lett. 130, 40005 (2020) 
- 
								[50]
								L. H Wang and M. S Ma, Phys. Lett. B 831, 137181 (2022) 
- 
								[51]
								Y. Ladghami, B. Asfour, A. Bouali et al., Phys. Dark Univ. 44, 101470 (2024) 
- 
								[52]
								S. Rani, A. Jawad, and M. Hussain, Eur. Phys. J. C 83, 8 (2023) 
- 
								[53]
								C. V. Johnson, Mod. Phys. Lett. A 33, 1850175 (2018), arXiv: 1705.06154 
- 
								[54]
								M. Born, Proc. R. Soc. Lond. A 143, 849 (1934) 
- 
								[55]
								Y. Kats, L. Motl, and M. Padi, J. High Energ. Phys. 2007(12), 068 (2007) 
- 
								[56]
								D. Anninos and G. Pastras, J. High Energ. Phys. 07, 030 (2009), arXiv: 0807.3478 
- 
								[57]
								R. G. Cai, Z. Y. Nie, and Y. W. Sun, Phys. Rev. D 78, 126007 (2008), arXiv: 0811.1665 
- 
								[58]
								N. Seiberg and E. Witten, J. High Energ. Phys. 1999(09), 032 (1999), arXiv: hep-th/9908142 
- 
								[59]
								Paul A. M. Dirac, Lectures on Quantum Mechanics, Dover Books on Physics, Garden City, (New York: Dover Publications, 2013) 
- 
								[60]
								Z. Bialynicka-Birula and I. Bialynicki-Birula, Phys. Rev. D 2, 2341 (1970) 
- 
								[61]
								H. El Moumni, Phys. Lett. B 776, 124 (2018) 
- 
								[62]
								Y. Z Du, H. F Li, F. Liu et al., Chin. Phys. C 45, 115103 (2021) 
- 
								[63]
								D. Roychowdhury, Phys. Lett. B 718, 1089 (2013) 
- 
								[64]
								P. K. Yerra and C. Bhamidipati, Mod. Phys. Lett. A 34, 27 (2019), arXiv: 1806.08226 
- 
								[65]
								C. Tsallis, J. Statist. Phys. 52, 479 (1988) 
- 
								[66]
								C. Tsallis and L. J. L. Cirto, Eur. Phys. J. C 73, 2487 (2013) 
- 
								[67]
								K. Nozari and A. S. Sefiedgar, Gen. Relativ. Gravit. 39, 501 (2007), arXiv: gr-qc/0606046 
- 
								[68]
								K. Nozari and A.S. Sefiedgar, Phys. Lett. B 635, 156 (2006), arXiv: gr-qc/0601116 
- 
								[69]
								J. Neyman, Proceedings of the fourth Berkeley symposium on mathematical statistics and probability, (Berkeley: University of California Press, 1961) 
- 
								[70]
								A. Sayahian Jahromi, S. A. Moosavi, H. Moradpour, et al., Phys. Lett. B 780, 21 (2018) 
- 
								[71]
								G. Kaniadakis, Phys. Rev. E 72, 036108 (2005) 
- 
								[72]
								Y. Z Du, X. Y Liu, Y. Zhang et al., Eur. Phys. J. C 83(5), 426 (2023) 
- 
								[73]
								Y. Z Du, H. F Li, F. Liu et al., J. High Energ. Phys. 2023(01), 137 (2023), arXiv: 2204.05621 
- 
								[74]
								Y. Z Du, H. F Li, X. N Zhou et al., Chin. Phys. C 46, 122002 (2022), arXiv: 2206.14382 
- 
								[75]
								J. L Zhang, R. G Cai, and H. Yu, J. High Energ. Phys. 2015(02), 143 (2015) 
- 
								[76]
								F. McCarthy, D. Kubiznak, and R. B. Mann, J. High Energ. Phys. 2017(11), 165 (2017) 
- 
								[77]
								A. Chamblin, R. Emparan, C. V. Johnson et al., Phys. Rev. D 60, 104026 (1999) 
- 
								[78]
								G. Gibbons and S. Hawking, Phys. Rev. D 15(5), 2752 (1977) 
- 
								[79]
								A. B. Balakin, J. P. S. Lemos, and A. E. Zayats, Phys. Rev. D 93, 024008 (2016) 
- 
								[80]
								S. H Mazharimousavi and M. Halilsoy, Phys. Rev. D 76, 087501 (2007) 
- 
								[81]
								M. M. Stetsko, Phys. Rev. D 101, 124017 (2020) 
- 
								[82]
								L. Chakhchi, H. El Moumni, and K. Masmar, Phys. Rev. D 105, 064031 (2022) 
- 
								[83]
								Y. Z Du, H. F Li, Y. Zhang et al., Entropy 25(4), 687 (2023) 
- 
								[84]
								Y. Z Du and Q. Gu, Eur. Phys. J. C 84, 1025 (2024)