Immirzi parameter and quasinormal modes in four and higher spacetime dimensions

Abstract

There is a one-parameter quantization ambiguity in loop quantum gravity, which is called the Immirzi parameter. In this paper, we fix this free parameter by considering the quasinormal mode spectrum of black holes in four and higher spacetime dimensions. As a consequence, our result is consistent with the Bekenstein–Hawking entropy of a black hole. Moreover, we also give a possible quantum gravity explanation of the universal ln 3 behavior of the quasinormal mode spectrum.

Keywords

Immirzi parameter / quasinormal mode / loop quantum gravity

References

[1] C. Rovelli, Quantum Gravity, Cambridge University Press, 2004

[2] T. Thiemann, Modern Canonical Quantum General Relativity, Cambridge University Press, 2007

[3] A. Ashtekar and J. Lewandowski, Background independent quantum gravity: A status report, Class. Quantum Gravity 21(15), R53 (2004)

[4] M. Han, Y. Ma, and W. Huang, Fundamental structure of loop quantum gravity, Int. J. Mod. Phys. D 16(09), 1397 (2007)

[5] A. Ashtekar and P. Singh, Loop quantum cosmology: A status report, Class. Quantum Gravity 28(21), 213001 (2011)

[6] C. Rovelli, Loop quantum gravity: The first 25 years, Class. Quantum Gravity 28(15), 153002 (2011)

[7] J. Barbero and A. Perez, Quantum geometry and black holes, arXiv: 1501.02963

[8] C. Rovelli and T. Thiemann, Immirzi parameter in quantum general relativity, Phys. Rev. D 57(2), 1009 (1998)

[9] O. Dreyer, Quasinormal modes, the area spectrum, and black hole entropy, Phys. Rev. Lett. 90(8), 081301 (2003)

[10] S. Hod, Bohr's correspondence principle and the area spectrum of quantum black holes, Phys. Rev. Lett. 81(20), 4293 (1998)

[11] L. Motl, An analytical computation of asymptotic Schwarzschild quasinormal frequencies, Adv. Theor. Math. Phys. 6, 1135 (2003)

[12] A. Corichi, Quasinormal modes, black hole entropy, and quantum geometry, Phys. Rev. D 67(8), 087502 (2003)

[13] Y. Ling and H. Zhang, Quasinormal modes prefer supersymmetry? Phys. Rev. D 68(10), 101501 (2003)

[14] L. Motl and A. Neitzke, Asymptotic black hole quasinormal frequencies, Adv. Theor. Math. Phys. 7(2), 307 (2003)

[15] V. Cardoso, J. Lemos, and S. Yoshida, Quasinormal modes of Schwarzschild black holes in four and higher dimensions, Phys. Rev. D 69(4), 044004 (2004)

[16] N. Bodendorfer, T. Thiemann, and A. Thurn, New variables for classical and quantum gravity in all dimensions (I): Hamiltonian analysis, Class. Quantum Gravity 30(4), 045001 (2013)

[17] N. Bodendorfer, T. Thiemann, and A. Thurn, New variables for classical and quantum gravity in all dimensions (II): Lagrangian analysis, Class. Quantum Gravity 30(4), 045002 (2013)

[18] N. Bodendorfer, T. Thiemann, and A. Thurn, New variables for classical and quantum gravity in all dimensions (III): Quantum theory, Class. Quantum Gravity 30(4), 045003 (2013)

[19] N. Bodendorfer, T. Thiemann, and A. Thurn, New variables for classical and quantum gravity in all dimensions (IV): Matter coupling, Class. Quantum Gravity 30(4), 045004 (2013)

[20] N. Bodendorfer, Black hole entropy from loop quantum gravity in higher dimensions, Phys. Lett. B 726(4-5), 887 (2013)

[21] X. Zhang, Higher dimensional loop quantum cosmology, arXiv: 1506.05597

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Higher Education Press and Springer-Verlag Berlin Heidelberg