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Acoustic black holes: massless scalar field analytic solutions and analogue Hawking radiation

  • H. S. Vieira
  • V. B. Bezerra
Research Article

Abstract

We obtain the analytic solutions of the radial part of the massless Klein–Gordon equation in the spacetime of both three dimensional rotating and four dimensional canonical acoustic black holes, which are given in terms of the confluent Heun functions. From these solutions, we obtain the scalar waves near the acoustic horizon. We discuss the analogue Hawking radiation of massless scalar particles and the features of the spectrum associated with the radiation emitted by these acoustic black holes.

Keywords

Massless Klein–Gordon equation Rotating acoustic black hole Canonical acoustic black hole Confluent Heun function Black body radiation 

Notes

Acknowledgments

The authors would like to thank Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) for partial financial support.

References

  1. 1.
    Unruh, W.G.: Phys. Rev. Lett. 46, 1351 (1981)ADSCrossRefGoogle Scholar
  2. 2.
    Hawking, S.W.: Commun. Math. Phys. 43, 199 (1975)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Banerjee, R., Kiefer, C., Majhi, B.R.: Phys. Rev. D 82, 044013 (2010)ADSCrossRefGoogle Scholar
  4. 4.
    Umetsu, K.: Phys. Lett. B 692, 61 (2010)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    Yale, A.: Phys. Lett. B 697, 398 (2011)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    Vieira, H.S., Bezerra, V.B., Costa, A.A.: Europhys. Lett. 109, 60006 (2015)ADSCrossRefGoogle Scholar
  7. 7.
    Barceló, C., Liberati, S., Visser, M.: Living Rev. Relat. 8, 12 (2005)ADSGoogle Scholar
  8. 8.
    Rousseaux, G., Mathis, C., Maïssa, P., Philbin, T.G., Leonhardt, U.: New J. Phys. 10, 053015 (2008)ADSCrossRefGoogle Scholar
  9. 9.
    Weinfurtner, S., Tedford, E.W., Penrice, M.C.J., Unruh, W.G., Lawrence, G.A.: Phys. Rev. Lett. 106, 021302 (2011)ADSCrossRefGoogle Scholar
  10. 10.
    Michel, F., Parentani, R.: Phys. Rev. D 90, 044033 (2014)ADSCrossRefGoogle Scholar
  11. 11.
    Garay, L.J., Anglin, J.R., Cirac, J.I., Zoller, P.: Phys. Rev. Lett. 85, 4643 (2000)ADSCrossRefGoogle Scholar
  12. 12.
    Fedichev, P.O., Fischer, U.R.: Phys. Rev. Lett. 91, 240407 (2003)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    Zapata, I., Albert, M., Parentani, R., Sols, F.: New J. Phys. 13, 063048 (2011)ADSCrossRefGoogle Scholar
  14. 14.
    Lahav, O., Itah, A., Blumkin, A., Gordon, C., Rinott, S., Zayats, A., Steinhauer, Jeff: Phys. Rev. Lett. 105, 240401 (2010)ADSCrossRefGoogle Scholar
  15. 15.
    Jacobson, T.A., Volovik, G.E.: Phys. Rev. D 58, 064021 (1998)ADSCrossRefGoogle Scholar
  16. 16.
    Ge, X.H., Sin, S.J.: J. High Energy Phys. 06, 087 (2010)ADSCrossRefGoogle Scholar
  17. 17.
    Ge, X.H., Wu, S.F., Wang, Y., Yang, G.H., Shen, Y.G.: Int. J. Mod. Phys. D 21, 1250038 (2012)ADSCrossRefGoogle Scholar
  18. 18.
    Gerace, D., Carusotto, I.: Phys. Rev. B 86, 144505 (2012)ADSCrossRefGoogle Scholar
  19. 19.
    Giovanazzi, S.: Phys. Rev. Lett. 94, 061302 (2005)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    Schützhold, R., Unruh, W.G.: Phys. Rev. Lett. 107, 149401 (2011)ADSCrossRefGoogle Scholar
  21. 21.
    Belgiorno, F., Cacciatori, S.L., Clerici, M., Gorini, V., Ortenzi, G., Rizzi, L., Rubino, E., Sala, V.G., Faccio, D.: Phys. Rev. Lett. 107, 149402 (2011)ADSCrossRefGoogle Scholar
  22. 22.
    Liberati, S., Prain, A., Visser, M.: Phys. Rev. D 85, 084014 (2012)ADSCrossRefGoogle Scholar
  23. 23.
    Finazzi, S., Carusotto, I.: Eur. Phys. J. Plus 127, 78 (2012)CrossRefGoogle Scholar
  24. 24.
    Marino, F.: Phys. Rev. A 78, 063804 (2008)ADSCrossRefGoogle Scholar
  25. 25.
    Marino, F., Ciszak, M., Ortolan, A.: Phys. Rev. A 80, 065802 (2009)ADSCrossRefGoogle Scholar
  26. 26.
    Fouxon, I., Farberovich, O.V., Bar-Ad, S., Fleurov, V.: Europhys. Lett. 92, 14002 (2010)ADSCrossRefGoogle Scholar
  27. 27.
    Solnyshkov, D.D., Flayac, H., Malpuech, G.: Phys. Rev. B 84, 233405 (2011)ADSCrossRefGoogle Scholar
  28. 28.
    Rubino, E., Belgiorno, F., Cacciatori, S.L., Clerici, M., Gorini, V., Ortenzi, G., Rizzi, L., Sala, V.G., Kolesik, M., Faccio, D.: New J. Phys. 13, 085005 (2011)ADSCrossRefGoogle Scholar
  29. 29.
    Steinhauer, J.: Nat. Phys. 10, 864 (2014)CrossRefGoogle Scholar
  30. 30.
    Fabbri, A., Mayoral, C.: Phys. Rev. D 83, 124016 (2011)ADSCrossRefGoogle Scholar
  31. 31.
    Mayoral, C., Fabbri, A., Rinaldi, M.: Phys. Rev. D 83, 124047 (2011)ADSCrossRefGoogle Scholar
  32. 32.
    Carusotto, I., Fagnocchi, S., Recati, A., Balbinot, R., Fabbri, A.: New J. Phys. 10, 103001 (2011)CrossRefGoogle Scholar
  33. 33.
    Steinhauer, J.: Phys. Rev. D 92, 024043 (2015)ADSCrossRefGoogle Scholar
  34. 34.
    Barceló, C., Liberati, S., Visser, M.: Class. Quantum Gravit. 18, 1137 (2001)ADSCrossRefGoogle Scholar
  35. 35.
    Visser, M., Barceló, C., Liberati, S.: Gen. Relativ. Gravit. 34, 1719 (2002)CrossRefGoogle Scholar
  36. 36.
    Das, S.R., Ghosh, A., Oh, J.H., Shapere, A.D.: J. High Energy Phys. 04, 030 (2011)ADSMathSciNetCrossRefGoogle Scholar
  37. 37.
    Robertson, S.J.: J. Phys. B: At. Mol. Opt. Phys. 45, 163001 (2012)ADSCrossRefGoogle Scholar
  38. 38.
    Wüster, S.: Phys. Rev. A 78, 021601(R) (2008)ADSCrossRefGoogle Scholar
  39. 39.
    Belenchia, A., Liberati, S., Mohd, A.: Phys. Rev. D 90, 104015 (2014)ADSCrossRefGoogle Scholar
  40. 40.
    Oliveira, E.S., Dolan, S.R., Crispino, L.C.B.: Phys. Rev. D 81, 124013 (2010)ADSCrossRefGoogle Scholar
  41. 41.
    Dolan, S.R., Oliveira, E.S., Crispino, L.C.B.: Phys. Rev. D 79, 064014 (2009)ADSMathSciNetCrossRefGoogle Scholar
  42. 42.
    Berti, E., Cardoso, V., Lemos, J.P.S.: Phys. Rev. D 70, 124006 (2004)ADSMathSciNetCrossRefGoogle Scholar
  43. 43.
    Unruh, W.G.: Phys. Rev. D 51, 2827 (1995)ADSMathSciNetCrossRefGoogle Scholar
  44. 44.
    Jacobson, T.: Phys. Rev. D 44, 1731 (1991)ADSMathSciNetCrossRefGoogle Scholar
  45. 45.
    Jacobson, T.: Phys. Rev. D 48, 728 (1993)ADSMathSciNetCrossRefGoogle Scholar
  46. 46.
    Basak, S., Majumdar, P.: Class. Quantum Gravit. 20, 3907 (2003)ADSMathSciNetCrossRefGoogle Scholar
  47. 47.
    Basak, S., Majumdar, P.: Class. Quantum Gravit. 20, 2929 (2003)ADSMathSciNetCrossRefGoogle Scholar
  48. 48.
    Lepe, S., Saavedra, J.: Phys. Lett. B 617, 174 (2005)ADSMathSciNetCrossRefGoogle Scholar
  49. 49.
    Slavyanov, S.Y., Lay, W.: Special Functions, a Unified Theory Based on Singularities. Oxford University Press, New York (2000)zbMATHGoogle Scholar
  50. 50.
    Hartle, J.B., Hawking, S.W.: Phys. Rev. D 13, 2188 (1976)ADSCrossRefGoogle Scholar
  51. 51.
    Christensen, S.M., Fulling, S.A.: Phys. Rev. D 15, 2088 (1977)ADSCrossRefGoogle Scholar
  52. 52.
    Robinson, S.P., Wilczek, F.: Phys. Rev. Lett. 95, 011303 (2005)ADSMathSciNetCrossRefGoogle Scholar
  53. 53.
    Parikh, M.K., Wilczek, F.: Phys. Rev. Lett. 85, 5042 (2000)ADSMathSciNetCrossRefGoogle Scholar
  54. 54.
    Kim, W., Shin, H.: J. High Energy Phys. 07, 070 (2007)ADSMathSciNetCrossRefGoogle Scholar
  55. 55.
    Bécar, R., González, P., Pulgar, G., Saavedra, J.: Int. J. Mod. Phys. A 25, 1463 (2010)ADSCrossRefGoogle Scholar
  56. 56.
    Zhang, L.C., Li, H.F., Zhao, R.: Phys. Lett. B 698, 438 (2011)ADSMathSciNetCrossRefGoogle Scholar
  57. 57.
    Anacleto, M.A., Brito, F.A., Passos, E.: Phys. Lett. B 694, 149 (2010)ADSMathSciNetCrossRefGoogle Scholar
  58. 58.
    Visser, M.: Class. Quantum Gravit. 15, 1767 (1998)ADSMathSciNetCrossRefGoogle Scholar
  59. 59.
    Ronveaux, A.: Heun’s Differential Equations. Oxford University Press, New York (1995)zbMATHGoogle Scholar
  60. 60.
    Fiziev, P.P.: J. Phys. A: Math. Theor. 43, 035203 (2010)ADSMathSciNetCrossRefGoogle Scholar
  61. 61.
    Vieira, H.S., Bezerra, V.B., Muniz, C.R.: Ann. Phys. 350, 14 (2014)ADSMathSciNetCrossRefGoogle Scholar
  62. 62.
    Damour, T., Ruffini, R.: Phys. Rev. D 14, 332 (1976)ADSCrossRefGoogle Scholar
  63. 63.
    Sannan, S.: Gen. Relativ. Gravit. 20, 239 (1988)ADSMathSciNetCrossRefGoogle Scholar
  64. 64.
    M. Visser. arXiv:gr-qc/9901047 (1999)
  65. 65.
    Arfken, G.B., Weber, H.J.: Mathematical Methods for Physicists. Elsevier, San Diego (2005)zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Departamento de FísicaUniversidade Federal da ParaíbaJoão PessoaBrazil
  2. 2.Centro de Ciências, Tecnologia e SaúdeUniversidade Estadual da ParaíbaArarunaBrazil

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