Research PapersNo Access

Zitterbewegung near a Schwarzschild-type black hole

Alexander V. Zhukov

Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372, Singapore

E-mail Address: alex_zhukov@sutd.edu.sg

Search for more papers by this author

Roland Bouffanais

Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372, Singapore

Search for more papers by this author

Natalia N. Konobeeva

Volgograd State University, 400062 Volgograd, Russia

Search for more papers by this author

, and

Mikhail B. Belonenko

Volgograd State University, 400062 Volgograd, Russia

Laboratory of Nanotechnology, Volgograd Institute of Business, 400048 Volgograd, Russia

Search for more papers by this author

https://doi.org/10.1142/S0217732316501686Cited by:2 (Source: Crossref)

Abstract

In this paper, we present an approximate analytic solution to the Dirac equation in the Schwarzschild geometry to investigate the Zitterbewegung (ZB) effect. The analytical expression for the current density, which is induced by the motion of a wave packet of electrons, is obtained. In addition, the intensity of dipole radiation near the black hole is calculated. The proposed approach is based on the Schrödinger representation, thereby allowing to consider the ZB effect in the case of a curved space. The considered example demonstrates a possibility for applying this approach to astrophysical applications, in particular to problems of the electron radiation in the vicinity of real black holes.

Keywords:

PACS: 03.65.Pm, 03.65.Ta, 04.70.-s

References

1. D. Chowdhury, S. Raju, S. Sachdev, A. Singh and Ph. Strack, Phys. Rev. B 87, 085138 (2013). Crossref, Web of Science, ADS, Google Scholar
2. C. Charmousis, B. Gouteraux, B. S. Kim, E. Kiritsis and R. Mayer, JHEP 1011, 151 (2010). Crossref, Web of Science, ADS, Google Scholar
3. G. Policastro, D. T. Son and A. O. Starinets, JHEP 9, 43 (2002). Crossref, Web of Science, ADS, Google Scholar
4. Sh. S. Pal, Phys. Rev. D 84, 126009 (2011). Crossref, Web of Science, ADS, Google Scholar
5. H. P. Nollert, Class. Quantum Grav. 16, R159 (1999). Crossref, Web of Science, ADS, Google Scholar
6. S. Chandrasekhar, The Mathematical Theory of Black Holes (Oxford Univ. Press, 1983). Google Scholar
7. N. N. Konobeeva and M. B. Belonenko, Phys. B: Condens. Matter 456, 115 (2014). Crossref, Web of Science, ADS, Google Scholar
8. R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt and C. F. Roos, Nature 463, 68 (2010). Crossref, Web of Science, ADS, Google Scholar
9. N. N. Konobeeva, A. A. Polunina and M. B. Belonenko, Int. J. Theor. Phys., Group Theory Nonlinear Opt. 17, 197 (2015). Web of Science, Google Scholar
10. I. I. Cotaescu, C. Crucean and C. A. Sporea, Eur. Phys. J. C 76, 102 (2016). Crossref, Web of Science, ADS, Google Scholar
11. N. D. Birrell and P. C. W. Davis, Quantum Fields in Curved Space (Cambridge Univ. Press, 1982). Crossref, Google Scholar
12. S. R. Das, G. W. Gibbons and S. D. Mathur, Phys. Rev. Lett. 78, 417 (1997). Crossref, Web of Science, ADS, Google Scholar
13. L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Pergamon Press, 1965). Google Scholar
14. G. Beitme and A. Erdein, Higher Transcendental Functions (Nauka, 1973). Google Scholar