- 
								[1]
								E. Ayon-Beato and A. Garcia, Phys. Rev. Lett. 80, 5056-5059 (1998), arXiv:gr-qc/9911046 
- 
								[2]
								S. A. Hayward, Phys. Rev. Lett. 96, 031103 (2006), arXiv:gr-qc/0506126[gr-qc 
- 
								[3]
								S. Ansoldi, Spherical black holes with regular center: A Review of existing models including a recent realization with Gaussian sources, in Conference on Black Holes and Naked Singularities. 2, 2008. arXiv: 0802.0330[gr-qc] 
- 
								[4]
								M. A. Markov, Limiting density of matter as a universal law of nature, JETP Lett. (Engl. Transl.); (United States) 36 (9, 1982) 214-216. https://www.osti.gov/biblio/6268156. 
- 
								[5]
								V. P. Frolov, Phys. Rev. D 94(10), 104056 (2016), arXiv:1609.01758[gr-qc 
- 
								[6]
								S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time. Cambridge Monographs on Mathematical Physics, (Cambridge University Press, 2, 2011) 
- 
								[7]
								R. M. Wald, General Relativity, (University of Chicago Press, Chicago, USA, 1984) 
- 
								[8]
								C. W. Misner and A. H. Taub, A Singularity-free Empty Universe, Sov. Phys. JETP 28, 122 (1969) http://www.jetp.ras.ru/cgi-bin/dn/e_028_01_0122.pdf. 
- 
								[9]
								V. Kagramanova, J. Kunz, E. Hackmann et al., Phys. Rev. D 81, 124044 (2010), arXiv:1002.4342[gr-qc 
- 
								[10]
								G. J. Olmo, D. Rubiera-Garcia, and A. Sanchez-Puente, Phys. Rev. D 92(4), 044047 (2015), arXiv:1508.03272[hep-th 
- 
								[11]
								A. D. Sakharov, Sov. Phys. JETP 22, 241 (1966) 
- 
								[12]
								E. B. Gliner, Sov. Phys. JETP 22, 378 (1966) 
- 
								[13]
								A. Borde, Phys. Rev. D 55, 7615-7617 (1997), arXiv:gr-qc/9612057 
- 
								[14]
								I. Dymnikova, Gen. Rel. Grav. 24, 235-242 (1992) 
- 
								[15]
								J. M. Bardeen, Non-singular general-relativistic gravitational collapse, in Conference Proceedings of GR5, Tbilisi, USSR, vol. 174. 1968 
- 
								[16]
								E. Ayon-Beato and A. Garcia, Phys. Lett. B 493, 149-152 (2000), arXiv:gr-qc/0009077 
- 
								[17]
								Z.-Y. Fan and X. Wang, Phys. Rev. D 94, 124027 (2016), arXiv:1610.02636[gr-qc 
- 
								[18]
								E. Ayon-Beato and A. Garcia, Gen. Rel. Grav. 37, 635 (2005), arXiv:hep-th/0403229 
- 
								[19]
								P. Nicolini, Int. J. Mod. Phys. A 24, 1229-1308 (2009), arXiv:0807.1939[hep-th 
- 
								[20]
								C. Bambi and L. Modesto, Phys. Lett. B 721, 329-334 (2013), arXiv:1302.6075[gr-qc 
- 
								[21]
								L. Balart and E. C. Vagenas, Phys. Rev. D 90, 124045 (2014), arXiv:1408.0306[gr-qc 
- 
								[22]
								C. Lan, Y.-G. Miao, and Y.-X. Zang, Eur. Phys. J. C 82(3), 231 (2022), arXiv:2109.13556[gr-qc 
- 
								[23]
								C. Lan, Y.-G. Miao, and Y.-X. Zang, Simulations of physical regular black holes in fluids, arXiv: 2206.08694[gr-qc] 
- 
								[24]
								A. Bonanno and M. Reuter, Phys. Rev. D 62, 043008 (2000), arXiv:hep-th/0002196 
- 
								[25]
								K. A. Bronnikov and J. C. Fabris, Phys. Rev. Lett. 96, 251101 (2006), arXiv:gr-qc/0511109 
- 
								[26]
								L. Modesto, Phys. Rev. D 86, 044005 (2012), arXiv:1107.2403[hep-th 
- 
								[27]
								L. Modesto, J. W. Moffat, and P. Nicolini, Phys. Lett. B 695, 397-400 (2011), arXiv:1010.0680[gr-qc 
- 
								[28]
								C. Lan, Y.-G. Miao, and H. Yang, Nucl. Phys. B 971, 115539 (2021), arXiv:2008.04609[gr-qc 
- 
								[29]
								C. Lan and Y.-G. Miao, Gliner vacuum, self-consistent theory of ruppeiner geometry for regular black holes, arXiv: 2103.14413[gr-qc] 
- 
								[30]
								Z. Li and C. Bambi, JCAP 01, 041 (2014), arXiv:1309.1606[gr-qc 
- 
								[31]
								A. Abdujabbarov, M. Amir, B. Ahmedov et al., Phys. Rev. D 93(10), 104004 (2016), arXiv:1604.03809[gr-qc 
- 
								[32]
								A. Flachi and J. P. S. Lemos, Phys. Rev. D 87, 024034 (2013), arXiv:1211.6212[gr-qc 
- 
								[33]
								S. Fernando and J. Correa, Phys. Rev. D 86, 064039 (2012), arXiv:1208.5442[gr-qc 
- 
								[34]
								B. Toshmatov, A. Abdujabbarov, Z. Stuchlık et al., Phys. Rev. D 91(8), 083008 (2015), arXiv:1503.05737[gr-qc 
- 
								[35]
								K. A. Bronnikov, Phys. Rev. D 63, 044005 (2001), arXiv:gr-qc/0006014[gr-qc 
- 
								[36]
								K. A. Bronnikov, V. N. Melnikov, and H. Dehnen, Gen. Rel. Grav. 39, 973-987 (2007), arXiv:gr-qc/0611022 
- 
								[37]
								Y. Zhang and S. Gao, Class. Quant. Grav. 35(14), 145007 (2016), arXiv:1610.01237 [gr-qc 
- 
								[38]
								K. A. Bronnikov, R. A. Konoplya, and A. Zhidenko, Phys. Rev. D 86, 024028 (2012), arXiv:1205.2224[gr-qc 
- 
								[39]
								W. Berej, J. Matyjasek, D. Tryniecki et al., Gen. Rel. Grav. 38, 885-906 (2006), arXiv:hep-th/0606185 
- 
								[40]
								J. W. Moffat, Eur. Phys. J. C 75(4), 175 (2015), arXiv:1412.5424[gr-qc 
- 
								[41]
								S. Hod, Phys. Rev. Lett. 81, 4293 (1998), arXiv:gr-qc/9812002[gr-qc 
- 
								[42]
								M. Maggiore, Phys. Rev. Lett. 100(14), 141301 (2008), arXiv:0711.3145[gr-qc 
- 
								[43]
								G. Kunstatter, Phys. Rev. Lett. 90, 161301 (2003), arXiv:gr-qc/0212014[gr-qc 
- 
								[44]
								L. Motl and A. Neitzke, Adv. Theor. Math. Phys. 7(2), 307 (2003), arXiv:hep-th/0301173[hep-th 
- 
								[45]
								J. Natario and R. Schiappa, Adv. Theor. Math. Phys. 8(6), 1001 (2004), arXiv:hep-th/0411267[hep-th 
- 
								[46]
								E. Berti, V. Cardoso, and A. O. Starinets, Class. Quant. Grav. 26(16), 163001 (2009), arXiv:0905.2975[gr-qc 
- 
								[47]
								R. A. Konoplya and A. Zhidenko, Rev. Mod. Phys. 83(3), 793 (2011), arXiv:1102.4014[gr-qc 
- 
								[48]
								P. R. Giri, Int. J. Mod. Phys. A 22(11), 2047 (2007), arXiv:hep-th/0604188[hep-th 
- 
								[49]
								R. P. Geroch, Annals Phys. 48, 526-540 (1968) 
- 
								[50]
								B. V. Shabat, Introduction to Complex Analysis. Part 1: Functions of a single variable. URSS, 6th ed., 2020 
- 
								[51]
								A. A. Goldberg and I. V. Ostrovskii, Value distribution of meromorphic functions. Transl. Math. Monographs 236, (American. American Mathematical Soc., 2008) 
- 
								[52]
								E. Curiel, Einstein Stud. 13, 43-104 (2017), arXiv:1405.0403[physics.hist-ph 
- 
								[53]
								F. Moura and J. a. Rodrigues, JHEP 2021, 078 (2021), arXiv:2105.02616[hep-th 
- 
								[54]
								R. B. White, Asymptotic Analysis of Differential Equations, (Imperial College Press, Nov., 2005) 
- 
								[55]
								M. Nakahara, Geometry, Topology and Physics, (CRC Press, 2nd ed., June, 2003) 
- 
								[56]
								I. R. Shafarevich, Basic Algebraic Geometry 1, (Springer Berlin Heidelberg, 2013) https://doi.org/10.1007%2F978-3-642-37956-7. 
- 
								[57]
								M. V. Fedoryuk, Asymptotic Analysis, (Springer, 1993) 
- 
								[58]
								A. Peltola and G. Kunstatter, Phys. Rev. D 80, 044031 (2009), arXiv:0902.1746[gr-qc 
- 
								[59]
								J. Babb, R. Daghigh, and G. Kunstatter, Phys. Rev. D 84, 084031 (2011), arXiv:1106.4357[gr-qc 
- 
								[60]
								R. G. Daghigh, G. Kunstatter, and J. Ziprick, Class. Quant. Grav. 24, 1981-1992 (2007), arXiv:gr-qc/0611139 
- 
								[61]
								H. Culetu, Int. J. Theor. Phys. 54(8), 2855-2863 (2015), arXiv:1408.3334[gr-qc 
- 
								[62]
								F. W. Olver, D. W. Lozier, R. F. Boisvert et al., NIST handbook of mathematical functions hardback and CD-ROM, (Cambridge university press, 2010) 
- 
								[63]
								P. Nicolini, A. Smailagic, and E. Spallucci, Phys. Lett. B 632(4), 547 (2006), arXiv:gr-qc/0510112[gr-qc 
- 
								[64]
								N. Andersson and C. J. Howls, Class. Quant. Grav. 21(6), 1623 (2004), arXiv:gr-qc/0307020[gr-qc