Skip to main content
SpringerLink
Log in

Gravitational anomalies and entropy

  • Research Article
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

Abstract

A derivation of entropy from the expressions for two dimensional gravitation anomalies is given. Starting from the near horizon anomalous energy–momentum tensors corresponding to particular anomalies, the Virasoro algebra with central extension is obtained. The central charge is identified by comparing with the standard form of the algebra. Then the conserved charge in the ground state is computed. Finally, using the Cardy formula the entropy is obtained. Here both the vector and chiral theories are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. For more details and several important issues, see [17–19].

  2. For a Hamiltonian or Lagrangian approach and its related issues to find the Virasoro algebra, see [26–67].

References

  1. Hawking, S.W.: Nature 248, 30 (1974)

    ADS  Google Scholar 

  2. Bekenstein, J.D.: Phys. Rev. D 7, 2333 (1973)

    MathSciNet  ADS  Google Scholar 

  3. Ashtekar, A. Baez, J., Corichi, A. Krasnov, K.: Phys. Rev. Lett. 80, 904 (1998) [arXiv:gr-qc/9710007]

    Google Scholar 

  4. Garcia-Islas, J.M.: Class. Quantum Grav. 25, 245001 (2008) [arXiv:0804.2082 [gr-qc]]

  5. Strominger, A., Vafa, C.: Phys. Lett. B 379, 99 (1996) [arXiv:hep-th/9601029]

  6. Brown, J.D., Henneaux, M.: Commun. Math. Phys. 104, 207 (1986)

    MathSciNet  ADS  MATH  Google Scholar 

  7. Strominger, A.: JHEP 9802, 009 (1998) [arXiv:hep-th/9712251]

  8. Davies, P.C.W., Fulling, S.A.: Proc. R. Soc. Lond. A 354, 59 (1977)

    MathSciNet  ADS  Google Scholar 

  9. Alvarez-Gaume, L., Witten, E.: Nucl. Phys. B234, 269 (1984)

    MathSciNet  ADS  Google Scholar 

  10. Bardeen, W.A., Zumino, B.: Nucl. Phys. B 244, 421 (1984)

    MathSciNet  ADS  Google Scholar 

  11. Bertlmann, R. A., Kohlprath, E.: Ann. Phys. 288, 137 (2001) [arXiv:hep-th/0011067]

  12. Christensen, S.M., Fulling, S.A.: Phys. Rev. D 15, 2088 (1977)

    ADS  Google Scholar 

  13. Robinson, S.P., Wilczek, F.: Phys. Rev. Lett. 95, 011303 (2005) [arXiv:gr-qc/0502074]

    Google Scholar 

  14. Iso, S., Umetsu, H., Wilczek, F.: Phys. Rev. Lett. 96, 151302 (2006) [arXiv:hep-th/0602146]

    Google Scholar 

  15. Umetsu, K.: Int. J. Mod. Phys. A 25, 4123 (2010) [arXiv:0907.1420 [hep-th]]

  16. Banerjee, R., Kulkarni, S.: Phys. Rev. D 77, 024018 (2008) [arXiv:0707.2449 [hep-th]]

  17. Banerjee, R., Kulkarni, S.: Phys. Lett. B 659, 827 (2008) [arXiv:0709.3916 [hep-th]]

  18. Banerjee, R., Kulkarni, S.: Phys. Rev. D 79, 084035 (2009) [arXiv:0810.5683 [hep-th]]

  19. Banerjee, R. Majhi, B.R.: Phys. Rev. D 79, 064024 (2009) [arXiv:0812.0497 [hep-th]]

  20. Akhmedova, V., Pilling, T., de Gill, A., Singleton, D.: Phys. Lett. B 673, 227 (2009) [arxiv:0808.3413 [hep-th]]

  21. Zampeli, A., Singleton, D., Vagenas, E.C.: JHEP 1206, 097 (2012) [arxiv:1206.0879 [gr-qc]]

  22. Coussaert, O., Henneaux, M., van Driel, P.: Class. Quantun Grav. 12, 2961 (1995) [arXiv:gr-qc/9506019]

  23. Solodukhin, S.N.: Phys. Lett. B 454, 213 (1999) [arXiv:hep-th/9812056]

  24. Cardy, J.L.: Nucl. Phys. B 270, 186 (1986)

    MathSciNet  ADS  MATH  Google Scholar 

  25. Bloete, H.W.J., Cardy, J.L., Nightingale, M.P.: Phys. Rev. Lett. 56, 742 (1986)

    ADS  Google Scholar 

  26. Carlip, S.: Phys. Rev. Lett. 82, 2828 (1999) [arXiv:hep-th/9812013]

    Google Scholar 

  27. Carlip, S.: Class. Quantum Grav. 16, 3327 (1999) [arXiv:gr-qc/9906126]

  28. Lin, F.L., Wu, Y.S.: Phys. Lett. B 453, 222 (1999) [arXiv:hep-th/9901147]

  29. Solovev, V.O.: Phys. Rev. D 61, 027502 (2000) [arXiv:hep-th/9905220]

  30. Natsuume, M., Okamura, T., Sato, M.: Phys. Rev. D 61, 104005 (2000) [arXiv:hep-th/9910105]

  31. Navarro, D.J., Navarro-Salas, J., Navarro, P.: Nucl. Phys. B 580, 311 (2000) [arXiv:hep-th/9911091]

  32. Jing, J.L., Yan, M.L.: Phys. Rev. D 62, 104013 (2000) [arXiv:gr-qc/0004061]

  33. Das, S., Ghosh, A., Mitra, P.: Phys. Rev. D 63, 024023 (2001) [arXiv:hep-th/0005108]

  34. Jing, J.L., Yan, M.L.: Phys. Rev. D 63, 024003 (2001) [arXiv:gr-qc/0005105]

  35. Terashima, H.: Phys. Lett. B 499, 229 (2001) [arXiv:hep-th/0011010]

  36. Hotta, M., Sasaki, K., Sasaki, T.: Class. Quantum Grav. 18, 1823 (2001) [arXiv:gr-qc/0011043]

  37. Terashima, H.: Phys. Rev. D 64, 064016 (2001) [arXiv:hep-th/0102097]

  38. Koga, J.I.: Phys. Rev. D 64, 124012 (2001) [arXiv:gr-qc/0107096]

  39. Park, M.I.: Nucl. Phys. B 634, 339 (2002) [arXiv:hep-th/0111224]

  40. Carlip, S.: Phys. Rev. Lett. 88, 241301 (2002) [arXiv:gr-qc/0203001]

    Google Scholar 

  41. Cvitan, M., Pallua, S., Prester, P.: Phys. Lett. B 555, 248 (2003) [arXiv:hep-th/0212029]

  42. Medved, A.J.M., Martin, D., Visser, M.: Class. Quantum Grav. 21, 3111 (2004) [arXiv:gr-qc/0402069]

  43. Kang, G., Koga, J.I., Park, M.I.: Phys. Rev. D 70, 024005 (2004) [arXiv:hep-th/0402113]

  44. Giacomini, A.: Phys. Rev. D 70, 044005 (2004) [arXiv:hep-th/0403219]

  45. Cvitan, M., Pallua, S., Prester, P.: Phys. Rev. D 70, 084043 (2004) [arXiv:hep-th/0406186]

  46. Carlip, S.: Class. Quantum Grav. 22, 1303 (2005) [arXiv:hep-th/0408123]

  47. Cvitan, M., Pallua, S.: Phys. Rev. D 71, 104032 (2005) [arXiv:hep-th/0412180]

  48. Carlip, S.: Class. Quantum Grav. 22, R85 (2005) [arXiv:gr-qc/0503022]

  49. Carlip, S.: Phys. Rev. Lett. 99, 021301 (2007) [arXiv:gr-qc/0702107]

    Google Scholar 

  50. Carlip, S.: Gen. Relativ. Gravit. 39, 1519 (2007) [Int. J. Mod. Phys. D 17, 659 (2008)] [arXiv:0705.3024 [gr-qc]]

  51. Cao, L.M., Matsuo, Y., Tsukioka, T., Yoo, C.M.: Phys. Lett. B 679, 390 (2009) [arXiv:0906.2267 [hep-th]]

  52. Rodriguez, L., Yildirim, T.: Class. Quantum Grav. 27, 155003 (2010) [arXiv:1003.0026 [hep-th]]

  53. Button, B.K., Rodriguez, L., Whiting, C.A.: arXiv:1009.1661 [hep-th]

  54. Chung, H.: Phys. Rev. D 83, 084017 (2011) [arXiv:1011.0623 [gr-qc]]

  55. Guneratne, A., Rodriguez, L., Wickramasekara, S., Yildirim, T.: arXiv:1206.2261 [hep-th]

  56. Park, M.I., Ho, J.: Phys. Rev. Lett. 83, 5595 (1999) [arXiv:hep-th/9910158]

    Google Scholar 

  57. Carlip, S.: Phys. Rev. Lett. 83, 5596 (1999) [arXiv:hep-th/9910247]

    Google Scholar 

  58. Park, M.I., Yee, J.H.: Phys. Rev. D 61, 088501 (2000) [arXiv:hep-th/9910213]

  59. Dreyer, O., Ghosh, A., Wisniewski, J.: Class. Quantum Grav. 18, 1929 (2001) [arXiv:hep-th/0101117]

  60. Silva, S.: Class. Quantum Grav. 19, 3947 (2002) [arXiv:hep-th/0204179]

  61. Brustein, R.: Phys. Rev. Lett. 86, 576 (2001) [arXiv:hep-th/0005266]

    Google Scholar 

  62. Cvitan, M., Pallua, S., Prester, P.: Phys. Lett. B 546, 119 (2002) [arXiv:hep-th/0207265]

  63. Giacomini, A., Pinamonti, N.: JHEP 0302, 014 (2003) [arXiv:gr-qc/0301038]

  64. Pinamonti, N., Vanzo, L.: Phys. Rev. D 69, 084012 (2004) [arXiv:hep-th/0312065]

  65. Dias, G.A.S., Lemos, J.P.S.: Phys. Rev. D 74, 044024 (2006) [arXiv:hep-th/0602144]

  66. Majhi, B.R., Padmanabhan, T.: Phys. Rev. D 85, 084040 (2012) [arXiv:1111.1809 [gr-qc]]

  67. Majhi, B.R., Padmanabhan, T.: arXiv:1204.1422 [gr-qc]

  68. Russo, J.G.: Phys. Lett. B 359, 69 (1995) [hep-th/9507009]

  69. Deser, S., Duff, M.J., Isham, C.J.: Nucl. Phys. B 111, 45 (1976)

    MathSciNet  ADS  MATH  Google Scholar 

  70. Duff, M.J.: Nucl. Phys. B 125, 334 (1977)

    ADS  Google Scholar 

  71. Polyakov, A.M.: Phys. Lett. B 103, 207 (1981)

    MathSciNet  ADS  Google Scholar 

  72. Balbinot, R., Fabbri, A. Shapiro, I.L.: Nucl. Phys. B 559, 301 (1999) [arXiv:hep-th/9904162]

  73. Kolekar, S., Padmanabhan, T.: Phys. Rev. D 83, 064034 (2011) [arXiv:1012.5421 [gr-qc]]

  74. Leutwyler, H.: Phys. Lett. B 153, 65 (1985) [Erratum-ibid. 155B, 469 (1985)]

Download references

Author information

Authors and Affiliations

  1. IUCAA, Post Bag 4, Ganeshkhind, Pune University Campus, Pune, 411 007, India

    Bibhas Ranjan Majhi

Authors
  1. Bibhas Ranjan Majhi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bibhas Ranjan Majhi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Majhi, B.R. Gravitational anomalies and entropy. Gen Relativ Gravit 45, 345–357 (2013). https://doi.org/10.1007/s10714-012-1474-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10714-012-1474-9

Keywords

Search

Navigation