Investigación

 

Quasinormal frequencies of the Dirac field in a D-dimensional Lifshitz black hole

 

A. Lopez-Ortega

 

Departamento de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Unidad Profesional Adolfo López Mateos, Edificio 9, México, 07738 D. F, México, email: alopezo@esfm.ipn.mx

 

Received 27 May 2014;
Accepted 26 June 2014.

 

Abstract

In a D-dimensional Lifshitz black hole we calculate exactly the quasinormal frequencies of a test Dirac field in the massless and zero angular eigenvalue limits. These results are an extension of the previous calculations in which the quasinormal frequencies of the Dirac field are determined, but in four dimensions. We discuss the four-dimensional limit of our expressions for the quasinormal frequencies and compare with the previous results. We also determine whether the Dirac field has unstable modes in the D-dimensional Lifshitz spacetime.

Keywords: Quasinormal modes; Dirac field; Lifshitz spacetimes; classical stability.

 

PACS: 04.40.-b; 04.30.Nk; 04.70.Bw; 04.50.Gh

 

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Acknowledgments

I thank the support of CONACYT Mexico, SNI Mexico, EDI IPN, COFAAIPN, and Research Projects IPN SIP-20140832 and IPN SIP-20144150.

 

References

1. S. Kachru, X. Liu and M. Mulligan, Phys. Rev. D 78 (2008) 106005 [arXiv:0808.1725 [hep-th]         [ Links ]].

2. K. Balasubramanian and J. McGreevy, Phys. Rev. D 80 (2009) 104039. [arXiv:0909.0263 [hep-th]         [ Links ]].

3. K. D. Kokkotas and B. G. Schmidt, Living Rev. Rel. 2 (1999) 2. [arXiv:gr-qc/9909058]         [ Links ].

4. H. P. Nollert, Class. Quant. Grav. 16 (1999) R159.         [ Links ]

5. E. Berti, V. Cardoso and A. O. Starinets, Class. Quant. Grav. 26 (2009) 163001. [arXiv:0905.2975 [gr-qc]         [ Links ]].

6. R. A. Konoplya and A. Zhidenko, Rev. Mod. Phys. 83 (2011) 793. [arXiv:1102.4014 [gr-qc]         [ Links ]].

7. A. Giacomini, G. Giribet, M. Leston, J. Oliva and S. Ray, Phys. Rev. D 85 (2012) 124001. [arXiv: 1203.0582 [hep-th]         [ Links ]].

8. Y. S. Myung and T. Moon, Phys. Rev. D 86 (2012) 024006. [arXiv:1204.2116 [hep-th]         [ Links ]].

9. P. A. Gonzalez, J. Saavedra and Y. Vasquez, Int. J. Mod. Phys. D 21 (2012) 1250054. [arXiv:1201.4521 [gr-qc]         [ Links ]].

10. B. Cuadros-Melgar, J. de Oliveira and C. E. Pellicer, Phys. Rev. D 85 (2012) 024014 [arXiv:1110.4856 [hep-th]         [ Links ]].

11. P. A. Gonzalez, F. Moncada and Y. Vasquez, Eur. Phys. J. C 72 (2012) 2255. [arXiv:1205.0582 [gr-qc]         [ Links ]].

12. R. Becar, P A. Gonzalez and Y. Vasquez, Int. J. Mod. Phys. D 22 (2013) 1350007. [arXiv:1210.7561 [gr-qc]         [ Links ]].

13. S. Lepe, J. Lorca, F. Pena and Y. Vasquez, Phys. Rev. D 86 (2012) 066008. [arXiv:1205.4460 [hep-th]         [ Links ]].

14. M. Catalan, E. Cisternas, P. A. Gonzalez and Y. Vasquez, arXiv:1404.3172 [gr-qc].

15. M. Catalan, E. Cisternas, P. A. Gonzalez and Y. Vasquez, Eur. Phys. J. C 74 (2014) 2813. [arXiv:1312.6451 [gr-qc]         [ Links ]].

16. A. López-Ortega, Gen. Rel. Grav. 46 (2014) 1756. [arXiv:1406.0126 [gr-qc]         [ Links ]].

17. W. G. Unruh, Phys. Rev. D 10 (1974) 3194.         [ Links ]

18. W. G. Unruh, Phys. Rev. Lett. 31 (1973) 1265.         [ Links ]

19. M. Martellini and A. Treves, Phys. Rev. D 15 (1977) 3060.         [ Links ]

20. B. R. Iyer and A. Kumar, Phys. Rev. D 18 (1978) 4799.         [ Links ]

21. A. Lopez-Ortega, Int. J. Mod. Phys. D 9 (2009) 1441. [arXiv:0905.0073 [gr-qc]         [ Links ]].

22. A. López-Ortega, Gen. Rel. Grav. 39 (2007) 1011. [arXiv:0704.2468 [gr-qc]         [ Links ]].

23. R. Becar, P. A. Gonzalez and Y. Vasquez, Phys. Rev. D 89 (2014) 023001. [arXiv:1306.5974 [gr-qc]         [ Links ]].

24. A. Lopez-Ortega, Rev. Mex. Fis. 56 (2010) 44. [arXiv:1006.4906 [gr-qc]         [ Links ]].

25. G. W. Gibbons and A. R. Steif, Phys. Lett. B 314 (1993) 13. [arXiv:gr-qc/9305018]         [ Links ].

26. S. R. Das, G. W. Gibbons and S. D. Mathur, Phys. Rev. Lett. 78 (1997) 417. [arXiv:hep-th/9609052]         [ Links ].

27. I. I. Cotaescu, Mod. Phys. Lett. A 13 (1998) 2991. [arXiv:gr-qc/9808030]         [ Links ].

28. A. Lopez-Ortega, Lat. Am. J. Phys. Educ. 3 (2009) 578. [arXiv:0906.2754 [gr-qc]         [ Links ]].

29. N. Ginoux, The Dirac Spectrum (Lecture Notes in Mathematics Vol. 1976, Springer, Dordrecht, 2009).         [ Links ]

30. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Graphs, and Mathematical Table (Dover Publications, New York, 1965).         [ Links ]

31. Z. X. Wang and D. R. Guo, Special Functions (World Scientific Publishing, Singapore, 1989).         [ Links ]

32. F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark, NIST Handbook of Mathematical Functions, (Cambridge University Press, New York, 2010).         [ Links ]

33. A. Lopez-Ortega and I. Vega-Acevedo, Gen. Rel. Grav. 43 (2011)2631. [arXiv:1105.2802 [gr-qc]         [ Links ]].

34. R. Emparan and K. Tanabe, Phys. Rev. D 89 (2014) 064028, [arXiv:1401.1957 [hep-th]         [ Links ]].