Solutions of the Dirac Equation in a Bardeen Black Hole Geometry

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Abstract

In this paper we study the Dirac equation in the geometry of a (regular) Bardeen black hole. We will focus on finding new analytical solutions in the vicinity of the black hole horizon. These solutions can be used with the asymptotic solutions (derived in a previous paper) to compute numerical phase shifts that define the scattering amplitudes.

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  • [1] J. Polchinski String Thoery Vol. 2 Cambridge Univ. Press (2005).

  • [2] A. Ashtekar J. Pullin Loop Quantum GRavity: the first 30 years World Scientific (2017).

  • [3] A. Perez Living Rev. Relativ. (2013) 16:3.

  • [4] L. Freidel Int. J. Theor. Phys. (2005) 44: 1769.

  • [5] S. W. Hawking Comm. Math. Phys. 43 (1975) 199; Nature 248 (1974) 30-31.

  • [6] B. Mukhopadhyay S.K. Chakrabarti Class. Quantum Grav. 16 3165 (1999).

  • [7] I.I. Cotaescu Mod. Phys. Lett. A 22 (2007) 2493.

  • [8] W. G. Unruh Phys. Rev. D14 3251 (1976).

  • [9] A. Al-Badawi M.Q. Owaidat Gen Relativ Gravit 49:110 (2017).

  • [10] A. Zecca Nuovo Cimento 30 1309–1315 (1998).

  • [11] J. Jing Phys. Rev. D 70 065004 (2004); Phys. Rev. D 71 124006 (2005).

  • [12] D. Page Phys. Rev. D 14 1509 (1976).

  • [13] E. G. Kalnins and W. Miller J. Math. Phys. 33 286 (1992).

  • [14] F. Belgiorno S.L. Cacciatori J. Phys. A 42 135207 (2009)

  • [15] H. Schmid Math. Nachr. 2004 274–275 117–129.

  • [16] I. Sakalli and M. Halilsoy Phys. Rev. D 69 124012 (2004).

  • [17] G. -Ortigoza Gen. Relativ. Gravit. 5 395 (2001).

  • [18] H. Cebeci N. Ozdemir Class. Quantum Grav. 30 175005 (2013).

  • [19] F. Belgiorno S.L. Cacciatori J. Math. Phys. 51 033517 (2010).

  • [20] Yan Lyu and Song Cui Phys. Scr. 79 025001 (2009).

  • [21] J.M. Bardeen in: Conference Proceedings of GR5 Tbilisi USSR 1968 p. 174.

  • [22] Z.-Y. Fan and X. Wang Phys. Rev. D 94 124027 (2016).

  • [23] E. Ayon-Beato and A. Garcia Phys. Lett B 493 149 (2000).

  • [24] C.A. Sporea. Fermion scattering by a class of Bardeen black holes. arXiv:1806.11462

  • [25] B. Thaller The Dirac Equation Springer Verlag Berlin Heidelberg 1992.

  • [26] I.I. Cotaescu Mod. Phys. Lett. A 13 (1998) 2923-2936.

  • [27] D. R. Brill and J. A. Wheeler Rev. Mod. Phys. 29 (1957) 465.

  • [28] D. R. Brill and J. A. Cohen J. Math. Phys. 7 (1966) 238.

  • [29] D. G. Boulware Phys. Rev. D 12 (1975) 350.

  • [30] V. M. Villalba Mod. Phys. Lett. A 8 (1993) 2351-2364.

  • [31] I.I. Cotaescu Phys. Rev. D 60 (1999) 124006.

  • [32] I.I. Cotaescu J. Phys. A: Math. Gen. 33 (2000) 1977.

  • [33] I.I. Cotaescu Rom. J. Phys. 52 (2007) 895-940.

  • [34] C.A. Sporea Mod. Phys. Lett. A 30 1550145 (2015).

  • [35] I.I. Cotaescu C. Crucean and C.A. Sporea Eur. Phys. J. C (2016) 76:102.

  • [36] I.I. Cotaescu C. Crucean and C.A. Sporea Eur. Phys. J. C (2016) 76:413.

  • [37] C.A. Sporea Chinese Physics C Vol. 41 No. 12 (2017) 123101.

  • [38] V. B. Berestetski E. M. Lifshitz and L. P. Pitaevski. Quantum Electrodynamics. Pergamon Press Oxford 1982.

  • [39] I.D. Novikov Doctoral disertation Sthernberg Astronomical Institute (1963).

  • [40] I.I. Cotaescu C. Crucean Mod. Phys. Lett. A 22 (2008) 3707-3720.

  • [41] I.I. Cotaescu R. Racoceanu C. Crucean Mod. Phys. Lett. A 21 (2006) 1313-1318.

  • [42] F. W. J. Olver D. W. Lozier R. F. Boisvert and C. W. Clark NIST Handbook of Mathematical Functions (Cambridge University Press 2010).

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