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High overtones of Dirac perturbations of a Schwarzschild black hole

K. H. C. Castello-Branco^1,*, R. A. Konoplya^1,†, and A. Zhidenko^2,‡

¹Universidade de São Paulo, Instituto de Física, Caixa Postal 66318, 05315-970, São Paulo-SP, Brazil
²Department of Physics, Dniepropetrovsk National University, St. Naukova 13, Dniepropetrovsk 49050, Ukraine

^*Electronic address: karlucio@fma.if.usp.br
^†Electronic address: konoplya@fma.if.usp.br
^‡Electronic address: Z_A_V@ukr.net

Phys. Rev. D 71, 047502 – Published 10 February, 2005

DOI: https://doi.org/10.1103/PhysRevD.71.047502

Abstract

Using the Frobenius method, we find high overtones of the Dirac quasinormal spectrum for the Schwarzschild black hole. At high overtones, the spacing for imaginary part of $ω_{n}$ is equidistant and equals to $I m (ω_{n + 1}) - I m (ω_{n}) = i / 8 M$ , $M$ being the black hole mass, which is twice less than that for fields of integer spin. At high overtones, the real part of $ω_{n}$ goes to zero. This supports the suggestion that the expected correspondence between quasinormal modes and Barbero-Immirzi parameter in Loop Quantum Gravity is just a numerical coincidence.

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References (22)

K. Kokkotas and B. Schmidt, Living Rev. Relativity 2, 2 (1999); H-P. Nollert, Classical Quantum Gravity 16, 159 (1999).
G. T. Horowitz and V. Hubeny, Phys. Rev. D 62, 024027 (2000); D. Birmingham, I. Sachs, and S. N. Solodukhin, Phys. Rev. Lett. 88, 151301 (2002); A. Starinets, Phys. Rev. D 66, 124013 (2002); V. Cardoso, R. Konoplya, J. P. S. Lemosand , 68, 044024 (2003); E. Abdalla, B. Wang, A. Lima-Santos, and W. G. Qiu, Phys. Lett. B 538, 435 (2002); R. A. Konoplya, Phys. Rev. D 66, 044009 (2002); E. Abdalla, K. H. C. Castello-Branco, and A. Lima-Santos, 66, 104018 (2002).
S. Hod Phys. Rev. Lett. 81, 4293 (1998); O. Dreyer, 90, 081301 (2003).
E. Berti and K. D. Kokkotas, Phys. Rev. D 67, 064020 (2003); C. Molina, D. Guigno, E. Abdalla, and A. Saa, 69, 104013 (2004); R. A. Konoplya and A. Zhidenko, J. High Energy Phys. 06 (2004) 037; R. A.Konoplya, Phys. Rev. D 66, 084007 (2002); 70, 047503 (2004); G. Siopsis, hep-th/0409262;
V. Cardoso and J. P. S. Lemos, Phys. Rev. D 63, 124015 (2001);
H. T. Cho, Phys. Rev. D 68, 024003 (2003).
A. Zhidenko, Classical Quantum Gravity 21, 273 (2004).
Wei Zhou and Jian-Yang Zhu, Int. J. Mod. Phys. D 13, 1105 (2004).
S. Iyer and C. M. Will, Phys. Rev. D 35, 3621 (1987).
R. A.Konoplya, Phys. Rev. D 68, 024018 (2003).
N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space (Cambridge Univ. Press, Cambridge, England, 1982).
D. R. Brill and J. A. Wheeler, Rev. Mod. Phys. 29, 465 (1957); S. Chandrasekhar, The Mathematical Theory of Black Holes (Clarendon, Oxford, 1983).
E. M. Leaver, Proc. R. Soc. London A 402, 285 (1985).
H-P Nollert Phys. Rev. D 47 5253 (1993).
R. A. Konoplya, Phys. Rev. D 68, 124017 (2003);
T. R. Choudhury and T. Padmanabhan, Phys. Rev. D 69, 064033 (2004); A. J. M. Medved, D. Martin, and Matt Visser, Classical Quantum Gravity 21, 1393 (2004).
L. Motl, Adv. Theor. Math. Phys. 6, 1135 (2003); E. Berti and K. Kokkotas, Phys. Rev. D68, 044027 (2003).
L. Motl and A. Neitzke, Adv. Theor. Math. Phys. 7, 307 (2003); V. Cardoso, J. Lemos, and S. Yoshida, Phys. Rev. D 69, 044004 (2004).
E. Beri, V. Cardoso, and S. Yoshida, Phys. Rev. D 69, 124018 (2004); J. Natario and R. Schiappa, hep-th/0411267.
H. T. Cho and Y-C. Lin, gr-qc/0411090.
R. A. Konoplya, Phys. Lett. B 550, 117 (2002).
R. A. Konoplya and A. V. Zhidenko, gr-qc/0411059.

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High overtones of Dirac perturbations of a Schwarzschild black hole

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