Table of Contents Author Guidelines Submit a Manuscript
Advances in High Energy Physics
Volume 2015, Article ID 867601, 16 pages
http://dx.doi.org/10.1155/2015/867601
Review Article

Quasi-Normal Modes: The “Electrons” of Black Holes as “Gravitational Atoms”? Implications for the Black Hole Information Puzzle

1Physics Department, IURS “Santa Rita”, Via Trasaghis 18/E, 00188 Roma, Italy
2Austro-Ukrainian Institute for Science and Technology, Wiedner Hauptstrasse 8-10/136, 1040 Wien, Austria
3International Institute for Applicable Mathematics & Information Sciences (IIAMIS), B. M. Birla Science Centre, Adarsh Nagar, Hyderabad 500 463, India

Received 26 February 2015; Accepted 25 March 2015

Academic Editor: Maxim Khlopov

Copyright © 2015 Christian Corda. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.

Linked References

  1. S. W. Hawking, “Particle creation by black holes,” Communications in Mathematical Physics, vol. 43, no. 3, pp. 199–220, 1975. View at Publisher · View at Google Scholar · View at MathSciNet
  2. M. K. Parikh and F. Wilczek, “Hawking radiation as tunneling,” Physical Review Letters, vol. 85, no. 24, pp. 5042–5045, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. M. K. Parikh, “A secret tunnel through the horizon,” General Relativity and Gravitation, vol. 36, no. 11, pp. 2419–2422, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  4. R. Banerjee and B. R. Majhi, “Quantum tunneling beyond semiclassical approximation,” Journal of High Energy Physics, vol. 2008, article 095, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  5. M. Angheben, M. Nadalini, L. Vanzo, and S. Zerbini, “Hawking radiation as tunneling for extremal and rotating black holes,” Journal of High Energy Physics, vol. 2005, no. 5, article 014, 2005. View at Publisher · View at Google Scholar
  6. M. Arzano, A. J. M. Medved, and E. C. Vagenas, “Hawking radiation as tunneling through the quantum horizon,” Journal of High Energy Physics, vol. 2005, no. 9, article 037, 2005. View at Publisher · View at Google Scholar
  7. R. Banerjee and B. R. Majhi, “Hawking black body spectrum from tunneling mechanism,” Physics Letters. B, vol. 675, no. 2, pp. 243–245, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. C. Corda, “Non-strictly black body spectrum from the tunnelling mechanism,” Annals of Physics, vol. 337, pp. 49–54, 2013, definitive version corrected by typos, http://arxiv.org/abs/1305.4529. View at Publisher · View at Google Scholar
  9. C. Corda, “Time dependent Schrödinger equation for black hole evaporation: no information loss,” Annals of Physics, vol. 353, pp. 71–82, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  10. S. W. Hawking, “Breakdown of predictability in gravitational collapse,” Physical Review D, vol. 14, article 2460, 1976. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. C. Corda, “Effective temperature, hawking radiation and quasinormal modes,” International Journal of Modern Physics D, vol. 21, no. 11, Article ID 1242023, 11 pages, 2012. View at Publisher · View at Google Scholar
  12. C. Corda, “Effective temperature for black holes,” Journal of High Energy Physics, vol. 1108, p. 101, 2011. View at Google Scholar
  13. C. Corda, “Black hole quantum spectrum,” The European Physical Journal C, vol. 73, no. 12, 2013. View at Publisher · View at Google Scholar
  14. C. Corda, S. H. Hendi, R. Katebi, and N. O. Schmidt, “Effective state, Hawking radiation and quasi-normal modes for Kerr black holes,” Journal of High Energy Physics, vol. 2013, article 8, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  15. C. Corda, S. H. Hendi, R. Katebi, and N. O. Schmidt, “Hawking radiation-quasi-normal modes correspondence and effective states for nonextremal Reissner-Nordström black holes,” Advances in High Energy Physics, vol. 2014, Article ID 527874, 9 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. B. Zhang, Q.-Y. Cai, L. You, and M.-S. Zhan, “Hidden messenger revealed in Hawking radiation: a resolution to the paradox of black hole information loss,” Physics Letters B, vol. 675, no. 1, pp. 98–101, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  17. B. Zhang, Q.-y. Cai, M.-s. Zhan, and L. You, “Entropy is conserved in Hawking radiation as tunneling: a revisit of the black hole information loss paradox,” Annals of Physics, vol. 326, no. 2, pp. 350–363, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  18. B. Zhang, Q.-Y. Cai, M. S. Zhan, and L. You, “Noncommutative information is revealed from Hawking radiation as tunneling,” EPL, vol. 94, no. 2, Article ID 20002, 5 pages, 2011. View at Publisher · View at Google Scholar
  19. B. Zhang, Q.-Y. Cai, M. S. Zhan, and L. You, “Comment on ‘what the information loss is not’,” The Hadronic Journal, vol. 37, p. 75, 2014. View at Google Scholar
  20. B. Zhang, Q.-Y. Cai, M.-S. Zhan, and L. You, “Information conservation is fundamental: recovering the lost information in hawking radiation,” International Journal of Modern Physics D, vol. 22, no. 12, Article ID 1341014, 2013. View at Publisher · View at Google Scholar
  21. C. Corda, S. H. Hendi, R. Katebi, and N. O. Schmidt, “Initiating the effective unification of black hole horizon area and entropy quantization with quasi-normal modes,” Advances in High Energy Physics, vol. 2014, Article ID 530547, 12 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  22. N. Bohr, “I. On the constitution of atoms and molecules,” Philosophical Magazine Series 6, vol. 26, no. 151, pp. 1–25, 1913. View at Publisher · View at Google Scholar
  23. N. Bohr, “XXXVII. On the constitution of atoms and molecules,” Philosophical Magazine Series 6, vol. 26, no. 153, pp. 476–502, 1913. View at Publisher · View at Google Scholar
  24. N. Bohr, “Über die Serienspektra der Elemente,” Zeitschrift für Physik, vol. 2, no. 5, pp. 423–469, 1920. View at Publisher · View at Google Scholar · View at Scopus
  25. M. Maggiore, “Physical interpretation of the spectrum of black hole quasinormal modes,” Physical Review Letters, vol. 100, no. 14, Article ID 141301, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  26. S. Shankaranarayanan, “Do subleading corrections to Bekenstein-Hawking entropy hold the key to quantum gravity?” Modern Physics Letters A, vol. 23, no. 24, pp. 1975–1980, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  27. J. Zhang, “Black hole quantum tunnelling and black hole entropy correction,” Physics Letters B, vol. 668, no. 5, pp. 353–356, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  28. J. D. Bekenstein, “The quantum mass spectrum of the Kerr black hole,” Lettere Al Nuovo Cimento Series 2, vol. 11, no. 9, pp. 467–470, 1974. View at Publisher · View at Google Scholar · View at Scopus
  29. J. D. Bekenstein, “Quantum black holes as atoms,” in Proceedings of the Eight Marcel Grossmann Meeting on General Relativity, T. Piran and R. Ruffini, Eds., pp. 92–111, World Scientific, Singapore, 1999. View at Google Scholar
  30. C. W. Misner, K. S. Thorne, and J. Wheeler, Gravitation, W.H. Feeman and Company, New York, NY, USA, 1973. View at MathSciNet
  31. C. Corda, “A clarification on the debate on ‘the original Schwarzschild solution’,” Electronic Journal of Theoretical Physics, vol. 8, no. 25, pp. 65–82, 2011. View at Google Scholar
  32. A. E. Roy and D. Clarke, Astronomy: Principles and Practice, Taylor & Francis, 4th edition, 2003. View at Publisher · View at Google Scholar
  33. R. Banerjee and B. R. Majhi, “Quantum tunneling and trace anomaly,” Physics Letters. B, vol. 674, no. 3, pp. 218–222, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  34. S. W. Hawking, “The path integral approach to quantum gravity,” in General Relativity: An Einstein Centenary Survey, S. W. Hawking and W. Israel, Eds., Cambridge University Press, 1979. View at Google Scholar
  35. L. Motl, “An analytical computation of asymptotic Schwarzschild quasinormal frequencies,” Advances in Theoretical and Mathematical Physics, vol. 6, no. 6, pp. 1135–1162, 2003. View at Google Scholar · View at MathSciNet
  36. J. York Jr., “Dynamical origin of black-hole radiance,” Physical Review D, vol. 28, no. 12, pp. 2929–2945, 1983. View at Publisher · View at Google Scholar · View at MathSciNet
  37. S. Hod, “Bohr's correspondence principle and the area spectrum of quantum black holes,” Physical Review Letters, vol. 81, no. 20, pp. 4293–4296, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  38. S. Hod, “Gravitation, the quantum and bohr's correspondence principle,” General Relativity and Gravitation, vol. 31, no. 11, pp. 1639–1644, 1999. View at Publisher · View at Google Scholar
  39. H.-P. Nollert, “Quasinormal modes of Schwarzschild black holes: the determination of quasinormal frequencies with very large imaginary parts,” Physical Review D, vol. 47, no. 12, pp. 5253–5258, 1993. View at Publisher · View at Google Scholar · View at Scopus
  40. N. Andersson, “On the asymptotic distribution of quasinormal-mode frequencies for Schwarzschild black holes,” Classical and Quantum Gravity, vol. 10, no. 6, pp. L61–L67, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
  41. L. Motl and A. Neitzke, “Asymptotic black hole quasinormal frequencies,” Advances in Theoretical and Mathematical Physics, vol. 7, no. 2, pp. 307–330, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  42. R. J. Adler, P. Chen, and D. I. Santiago, “The generalized uncertainty principle and black hole remnants,” General Relativity and Gravitation, vol. 33, no. 12, pp. 2101–2108, 2001. View at Publisher · View at Google Scholar
  43. V. Mukhanov, “Are black holes quantized?” JETP Letters, vol. 44, no. 1, pp. 63–66, 1986. View at Google Scholar
  44. J. D. Bekenstein and V. F. Mukhanov, “Spectroscopy of the quantum black hole,” Physics Letters B, vol. 360, no. 1-2, pp. 7–12, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  45. G. 't Hooft, “The scattering matrix approach for the quantum black hole: an overview,” International Journal of Modern Physics A, vol. 11, no. 26, pp. 4623–4688, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  46. S. W. Hawking, “Information loss in black holes,” Physical Review D, vol. 72, Article ID 084013, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  47. L. Susskind, The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics, Little, Brown and Company, New York, NY, USA, 2008.
  48. A. Ananthaswamy, “Black Holes: Paradox Regained,” http://fqxi.org/community/articles/display/179?search=1.
  49. S. D. Mathur, “The information paradox: Conflicts and resolutions,” Pramana, vol. 79, no. 5, pp. 1059–1073, 2012. View at Publisher · View at Google Scholar
  50. S. W. Hawking, “Information preservation and weather forecasting for black holes,” http://arxiv.org/abs/1401.5761.
  51. J. J. Sakurai, Modern Quantum Mechanics, Pearson Education, 2006.
  52. R. Casadio and C. Germani, “Gravitational collapse and black hole evolution—do holographic black holes eventually ‘anti-evaporate’?” Progress of Theoretical Physics, vol. 114, no. 1, pp. 23–56, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  53. L. Sebastiani, D. Momeni, R. Myrzakulov, and S. D. Odintsov, “Instabilities and (anti)-evaporation of Schwarzschild–de Sitter black holes in modified gravity,” Physical Review D, vol. 88, no. 10, Article ID 104022, 17 pages, 2013. View at Publisher · View at Google Scholar
  54. T. Katsuragawa and S. Nojiri, “Stability and antievaporation of the Schwarzschild-de Sitter black holes in bigravity,” Physical Review D, vol. 91, Article ID 084001, 2015. View at Publisher · View at Google Scholar
  55. S. Nojiri and S. D. Odintsov, “Instabilities and anti-evaporation of Reissner–Nordström black holes in modified F(R) gravity,” Physics Letters B, vol. 735, pp. 376–382, 2014. View at Publisher · View at Google Scholar · View at MathSciNet