• [1]

    J. D. Bekenstein, Lett. Nuovo Cimento 4, 737 (1972)

  • [2]

    J. D. Bekenstein, Phys. Rev. D 7, 2333 (1973)

  • [3]

    J. D. Bekenstein, Phys. Rev. D 9, 3292 (1974)

  • [4]

    S. W. Hawking, Nature 248, 30 (1974)

  • [5]

    S. W. Hawking, Commun. Math. Phys. 43, 199 (1975)

  • [6]

    S. W. Hawking and D. N. Page, Commun. Math. Phys. 87, 577 (1983)

  • [7]

    A. Chamblin, R. Emparan, C. V. Johnson et al., Phys. Rev. D 60, 064018 (1999)

  • [8]

    A. Chamblin, R. Emparan, C. V. Johnson et al., Phys. Rev. D 60, 104026 (1999)

  • [9]

    B. P. Dolan, Class. Quantum Gravit. 28, 125020 (2011)

  • [10]

    D. Kubiznak and R. B. Mann, J. High Energy Phys. 07, 033 (2012)

  • [11]

    N. Altamirano, D. Kubizňák, and R. B. Mann, Phys. Rev. D 88, 101502 (2013)

  • [12]

    N. Altamirano, D. Kubizňák, R. B. Mann et al., Class.Quant.Grav. 31, 042001 (2014)

  • [13]

    S.-W. Wei and Y.-X. Liu, Phys. Rev. D 90, 044057 (2014)

  • [14]

    S.-W. Wei, P. Cheng, and Y.-X. Liu, Phys. Rev. D 93, 084015 (2016)

  • [15]

    S.-W. Wei and Y.-X. Liu, Phys. Rev. Lett. 115, 111302 (2015)

  • [16]

    S. H. Hendi, G.-Q. Li, J.-X. Mo et al., Eur. Phys. J. C 76, 571 (2016)

  • [17]

    S. H. Hendi, R. B. Mann, S. Panahiyan et al., Phys. Rev. D 95, 021501 (2017)

  • [18]

    P. K. Yerra, C. Bhamidipati, and S. Mukherji, Phys. Rev. D 106, 064059 (2022)

  • [19]

    S. W. Wei, Y.X. Liu, and R.B. Mann, Phys. Rev. Lett. 129, 191101 (2022)

  • [20]

    S. W. Wei and Y. X. Liu, Phys. Rev. D 105, 104003 (2022)

  • [21]

    D. Wu and S. Q. Wu, Phys. Rev. D 107, 084002 (2023)

  • [22]

    D. Wu, Phys. Rev. D 107, 024024 (2023)

  • [23]

    D. Wu, Eur. Phys. J. C 83, 365 (2023)

  • [24]

    D. Wu, Eur. Phys. J. C 83, 589 (2023)

  • [25]

    D. Wu, Phys. Rev. D 108, 084041 (2023)

  • [26]

    M.-Y. Zhang, H. Chen, H. Hassanabadi et al., Eur. Phys. J. C 83, 773 (2023)

  • [27]

    M.-Y. Zhang, H. Chen, H. Hassanabadi et al., arXiv: qr-qc/2312.12814

  • [28]

    A. Dehyadegari, A. Sheykhi, and A. Montakhab, Phys. Lett. B 768, 235 (2017)

  • [29]

    Z. Dayyani and A. Sheykhi, Phys. Rev. D 98, 104026 (2018)

  • [30]

    A. Dehyadegari, B.R. Majhi, A. Sheykhi et al., Phys. Lett. B 791, 30 (2019)

  • [31]

    K. Bhattacharya and B. R. Majhi, Phys. Lett. B 802, 135224 (2020)

  • [32]

    S. H. Hendi and K. Jafarzade, Phys. Rev. D 103, 104011 (2021)

  • [33]

    M.-Y. Zhang, H. Hassanabadi, H. Chen et al., Int. J. Mod. Phys. A 38, 2350087 (2023)

  • [34]

    Ö. Ökcü and E. Aydiner, Eur. Phys. J. C 77, 24 (2017)

  • [35]

    Ö. Ökcü and E. Aydiner, Eur. Phys. J. C 78, 123 (2018)

  • [36]

    H. Ghaffarnejad, E. Yaraie, and M. Farsam, Int. J. Theor. Phys. 57, 1671 (2018)

  • [37]

    J.-X. Mo, G.-Q. Li, S.-Q. Lan et al., Phys. Rev. D 98, 124032 (2018)

  • [38]

    Z.-W. Zhao, Y.-H. Xiu, and N. Li, Phys. Rev. D 98, 124003 (2018)

  • [39]

    D. M. Yekta, A. Hadikhani, and Ö. Ökcü, Phys. Lett. B 795, 521 (2019)

  • [40]

    M.-Y. Zhang, H. Chen, H. Hassanabadi et al., Chin. Phys. C 47, 045101 (2023)

  • [41]

    Y. Meng, J. Pu, and Q.-Q. Jiang, Chin. Phys. C 44, 065105 (2020)

  • [42]

    J. Liang, B. Mu, and P. Wang, Phys. Rev. D 104, 124003 (2021)

  • [43]

    M. Chabab, H. El Moumni, S. Iraoui et al., arXiv: 1804.10042v2 [gr-qc]

  • [44]

    J.-X. Mo and G.-Q. Li, Class. Quant. Grav. 37, 045009 (2020)

  • [45]

    C. L. A. Rizwan, A. N. Kumara, D. Vaid et al., Int. J. Mod. Phys. A 33, 1850210 (2019)

  • [46]

    D. Kastor, S. Ray, and J. Traschen, Class. Quant. Grav. 27, 235014 (2010)

  • [47]

    E. Komatsu, K M Smith, J Dunkley et al., Astrophys. J. Suppl. 192, 18 (2011)

  • [48]

    A.G. Riess, L.G. Strolger, J Tonry et al., The Astro. Phys. J. 607, 665 (2004)

  • [49]

    A. Y. Kamenshchik, U. Moschella, and V. Pasquier, Phys. Lett. B 511, 265 (2001)

  • [50]

    N. Bilic, G. B. Tupper, and R. D. Viollier, Phys. Lett. B 535, 17 (2002)

  • [51]

    M. C. Bento, O. Bertolami, and A. A. Sen, Phys. Rev. D 66, 043507 (2002)

  • [52]

    X.-Q. Li, B. Chen, and L.-l. Xing, Eur. Phys. J. Plus 135, 175 (2020)

  • [53]

    X.-Q. Li, B. Chen, and L.-l. Xing, Eur. Phys. J. Plus 137, 1167 (2022)

  • [54]

    X.-Q. Li, B. Chen, and L.-L. Xing, Annals Phys. 446, 169125 (2022)

  • [55]

    X.-Q. Li, H.-P. Yan, L.-L. Xing et al., Phys. Rev. D 107, 104055 (2023)

  • [56]

    X.-Q. Li, H.-P. Yan, X.-J. Yueet al., arXiv: gr-qc 2401.18066

  • [57]

    Y. Sekhmani, J. Rayimbaev, G.G. Luciano et al., Eur. Phys. J. C 84, 227 (2024)

  • [58]

    U. Debnath, A. Banerjee, and S. Chakraborty, Class. Quant. Grav. 21, 5609 (2004)

  • [59]

    I. Abramowitz, M. Stegun, Handbook of Mathematical Functions (1965)

  • [60]

    D. Kastor, S. Ray, and J. Traschen, Class. Quant. Grav. 26, 195011 (2009)

  • [61]

    S. Gunasekaran, R. B. Mann, and D. Kubiznak, J. High Energy Phys. 11, 110 (2012)

  • [62]

    D. Kubiznak, R. B. Mann, and M. Teo, Class. Quant. Grav. 34, 063001 (2017)

  • [63]

    R.-G. Cai and K.-S. Soh, Phys. Rev. D 59, 044013 (1999)

  • [64]

    H. B. Callen, 2nd ed., (John Wiley Sons, New York, 1985)

  • [65]

    K. Redlich and K. Zalewski, Acta. Physica Polonica B 47, 1943 (2016)

  • [66]

    B. Z. Maytal and A. Shavit, Cryogenics 37, 33 (1997)