• [1]

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

  • [2]

    B. P. Dolan, D. Kastor, D. Kubiznak et al., Phys. Rev. D 87, 104017 (2013)

  • [3]

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

  • [4]

    R. G. Cai, L.-M. Cao, L. Li et al., J. High Energy Phys. 09, 005 (2013)

  • [5]

    S. W. Wei, Y. X. Liu, and R. B. Mann, Phys. Rev. Lett. 123, 071103 (2019)

  • [6]

    R. G. Cai, L. Li, and S. H. T, Phys. Rev. D 105, 064032 (2022)

  • [7]

    J. L. Zhang, R. G. Cai, and H. W. Yu, Phys. Rev. D 91, 044028 (2015)

  • [8]

    Z. Y. Gao and L. Zhao, Class. Quantum Grav. 39, 075019 (2022)

  • [9]

    A. Karch and B. Robinson, J. High Energy Phys. 12, 073 (2015)

  • [10]

    M. Sinamuli and R. B. Mann, Phys. Rev. D 96, 086008 (2017)

  • [11]

    F. L. Lin and T. MatsuoE, Phys. Lett. B 641, 1 (2006)

  • [12]

    E. Witten, Adv. Theor. Math. Phys. 2, 505-532 (1998)

  • [13]

    C. Teitelboim, Phys. Lett. B 158, 293 (1985)

  • [14]

    M. Henneaux and C. Teitelboim, Phys. Lett. B 143, 415 (1984)

  • [15]

    J. Creighton and R.B. Mann, Phys. Rev. D 52, 4569 (1995)

  • [16]

    T. Padmanabhan, Class. Quant. Grav. 19, 5387 (2002)

  • [17]

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

  • [18]

    C. Singha, General Relativity and Gravitation 54, 38 (2022)

  • [19]

    G. E. Volovik, Mod. Phys. Lett. A, arXiv: 2107.11193

  • [20]

    C. Promsiri, E. Hirunsirisawat, and W. Liewrian, Phys. Rev. D 102, 064014 (2020)

  • [21]

    C. Promsiri, E. Hirunsirisawat, and W. Liewrian, Phys. Rev. D 104, 064004 (2021)

  • [22]

    R. Nakarachinda, E. Hirunsirisawat, L. Tannukij et al., Phys. Rev. D 104, 064003 (2021)

  • [23]

    A. Dehyadegari, A.d Sheykhi, and S. W. Wei, Phys. Rev. D 102, 104013 (2020)

  • [24]

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

  • [25]

    S. W. Wei, Y. X. Liu, and R. B. Mann, arXiv: 2108.07655

  • [26]

    S. W. Wei and Y. X. Liu, Commun. Theor. Phys 74, 095402 (2022)

  • [27]

    S. W. Wei and Y. X. Liu, Phys. Rev. D 104, 084087 (2021)

  • [28]

    S. W. Wei, Y. Q. Wang, Y. X. Liu et al., arXiv: 2102.00799

  • [29]

    S. W. Wei, Y. X. Liu, and R. B. Mann, Phys. Rev. D 100, 124033 (2019)

  • [30]

    Q. M. Fu, L. Zhao, and Y. X. Liu, Phys. Rev. D 104, 024033 (2021)

  • [31]

    R. Banerjee, B. R. Majhi, and S. Samanta, Phys. Lett. B 767, 10 (2017)

  • [32]

    R. Banerjee and D. Roychowdhury, J. High Energy Phys. 11, 004 (2011)

  • [33]

    R. Banerjee and D. R, Phys. Rev. D 85, 104043 (2012)

  • [34]

    K. Bhattacharya, B. R. Majhi, and S. Samanta, Phys. Rev. D 96, 084037 (2017)

  • [35]

    R. P. Singh, B. K. Singh, R. K. Gupta et al., Can. J. Phys. 100, 39-47 (2022)

  • [36]

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

  • [37]

    X. Y. Guo, H. F. Li, L. C. Zhang et al., Eur. Phys. J. C 80, 168 (2020)

  • [38]

    J. Liang, B. Mu, and J. Tao, Chinese. Phys. C 45, 023121 (2021)

  • [39]

    X. Y. Guo, H. F. Li, L. C. Zhang et al., Phys. Rev. D 100, 064036 (2019)

  • [40]

    L. Tannukij, P. Wongjun, E. Hirunsirisawat et al., Eur. Phys. J. Plus 135, 500 (2020)

  • [41]

    S. Mbarek and R. B. Mann, J. High Energy Phys. 02, 103 (2019)

  • [42]

    F. Simovic and R. B. Mann, Class. Quantum Grav. 36, 014002 (2019)

  • [43]

    D. Kubiznak and F. Simovic, Class. Quantum Grav. 33, 245001 (2016)

  • [44]

    Y. Sekiwa, Phys. Rev. D 73, 084009 (2006)

  • [45]

    M. Urano, A. Tomimatsu, and H. Saida, Class. Quant. Grav. 26, 105010 (2009)

  • [46]

    R. Clarkson and R. B. Mann, Class. Quant. Grav. 23, 1507 (2006)

  • [47]

    J. McInerney, G. Satishchandran, and J. Traschen, Class. Quantum Grav. 33, 105007 (2016)

  • [48]

    P. Kanti and T. Pappas, Phys. Rev. D 96, 024038 (2017)

  • [49]

    M. Chabab, H. E. Moumni, and J. Khalloufi, Nuclear Physics B 963, 115305 (2021)

  • [50]

    L. C. Zhang, R. Zhao, and M. S. Ma, Phys. Lett. B 761, 74 (2016)

  • [51]

    L. C. Zhang and R. Zhao, Phys. Lett. B 797, 134798 (2019)

  • [52]

    Y. B. Ma, Y. Zhang, L. C. Zhang et al., European Physical Journal C 80, 213 (2020)

  • [53]

    H. H. Zhao, L. C. Zhang, Y. Gao et al., Chin. Phys. C 45, 043111 (2021)

  • [54]

    X. Y. Guo, Y. Gao, H. F. Li et al., Phys. Rev. D 102, 124016 (2020)

  • [55]

    M. S. Ali1 and S. G. Ghosh, Eur. Phys. J. Plus 137, 486 (2022)

  • [56]

    N. Aghanim et al. (Planck Collaboration), Astron. Astrophys. 641, A6 (2020)

  • [57]

    S. Ponglertsakul and B. Gwak, European Physical Journal C 80, 1023 (2020)

  • [58]

    A. Ashtekar, B. Bonga, and A. Kesavan, Classical Quantum Gravity 32, 025004 (2015)

  • [59]

    R. M. Wald, Living. Rev. Rel. 4, 6 (2001)

  • [60]

    L. Gulin and I. Smolić, Class. Quantum Grav. 35, 025015 (2018)

  • [61]

    J. Oliva and S. Ray, Class. Quant. Grav. 29, 205008 (2012)

  • [62]

    R. A. Hennigar, E. Tjoa, and R. B. Mann, J. High Energ. Phys. 02, 70 (2017)

  • [63]

    G. Giribet, M. Leoni, J. Oliva et al., Phys. Rev. D 89, 085040 (2014)

  • [64]

    H. Dykaar, R. A. Hennigar, and R. B. Mann, J. High Energ. Phys. 05, 045 (2017)

  • [65]

    D. Magos and N. Breton, Phys. Rev. D 102, 084011 (2020)

  • [66]

    Smarr, Phys. Rev. Lett. 30, 71 (1973)

  • [67]

    N. Breton, Gen. Relativ. Gravit. 37, 643 (2005)

  • [68]

    D. Mitsios, T. Ortín, D. Pereñíguez et al., J. High Energy Phys. 08, 019 (2021)

  • [69]

    T. Ortin and Komar, J. High Energy Phys. 08, 023 (2021)

  • [70]

    K. Hajian, H. ¨Ozsahin, and B. Tekin, Phys. Rev. D 104, 044024 (2021)

  • [71]

    J. Cheyne and D. Mattingly, Phys. Rev. D 103, 086012 (2021)

  • [72]

    I. Prigogine and R. Defay, Chemical Thermodynamics (Longmans Green, New York, 1954).

  • [73]

    Prabhat K. Gupta, Cornelius T. Moynihan, J. Chem. Phys. 65, 4136 (1976)

  • [74]

    J. Jäckle, Models of the glass transition, Rep. Prog. Phys. 49, 171 (1986)

  • [75]

    J. X. Mo, G. Q. Li and W. B. Liu, Phys. Lett. B 730, 111 (2014)

  • [76]

    H. H. Zhao, L. C. Zhang, F. Liu et al., Commun. Theor. Phys. 73, 095401 (2021)