Skip to main content
Log in

Entanglement entropy due to near-horizon degrees of freedom

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

Assuming that the dominant contribution to the entropy due to entanglement across a spherical hypersurface comes from the near-horizon degrees of freedom, we analytically derive the entropy of a free massless scalar field in Minkowski spacetime across a spherical entangling surface. The resulting entanglement entropy is found to be proportional to the entangling surface as expected. A logarithmic subleading term with positive coefficient is also found through numerical computation. We have extended the analysis to higher dimensions as well.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. J.M. Bardeen, B. Carter, S.W. Hawking, Commun. Math. Phys. 31, 161 (1973).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. J.D. Bekenstein, Lett. Nuovo Cimento 4, 737 (1972).

    Article  ADS  Google Scholar 

  3. J.D. Bekenstein, Contemp. Phys. 45, 31 (2004).

    Article  ADS  Google Scholar 

  4. D.N. Page, New J. Phys. 7, 203 (2005).

    Article  MathSciNet  ADS  Google Scholar 

  5. J.W. York Jr., Phys. Rev. D 28, 2929 (1983).

    Article  MathSciNet  ADS  Google Scholar 

  6. G. t Hooft, Nucl. Phys. B 256, 727 (1985).

    Article  MathSciNet  ADS  Google Scholar 

  7. V.P. Frolov, I. Novikov, Phys. Rev. D 48, 4545 (1993) gr-qc/9309001.

    Article  MathSciNet  ADS  Google Scholar 

  8. A. Strominger, C. Vafa, Phys. Lett. B 379, 99 (1996) hep-th/9601029.

    Article  MathSciNet  ADS  Google Scholar 

  9. A. Ashtekar, J. Baez, A. Corichi, K. Krasnov, Phys. Rev. Lett. 80, 904 (1998).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. S. Carlip, Phys. Rev. Lett. 88, 241301 (2002) gr-qc/0203001.

    Article  MathSciNet  ADS  Google Scholar 

  11. S. Carlip, Class. Quantum. Grav. 17, 4175 (2000) gr-qc/0005017.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. R.K. Kaul, P. Majumdar, Phys. Rev. Lett. 84, 5255 (2000) gr-qc/0002040.

    Article  MathSciNet  ADS  Google Scholar 

  13. A. Sen, Gen. Rel. Grav. 40, 2249 (2008) arXiv:0708.1270 [hep-th].

    Article  ADS  MATH  Google Scholar 

  14. L. Bombelli, R.K. Koul, J.-H. Lee, R.D. Sorkin, Phys. Rev. D 34, 373 (1986).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. M. Srednicki, Phys. Rev. Lett. 71, 666 (1993).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. S. Das, S. Shankaranarayanan, S. Sur, Phys. Rev. D 77, 064013 (2008) gr-qc/0705.2070.

    Article  ADS  Google Scholar 

  17. S. Das, S. Shankaranarayanan, Class. Quantum. Grav. 24, 5299 (2007) gr-qc/0703082.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. S. Shankaranarayanan, Entropy 13, 11 (2011) arXiv:1101.0030 [gr-qc].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. R. Lohmayer, H. Neuberger, A. Schwimmer, S. Theisen, Phys. Lett. B 685, 222 (2010).

    Article  ADS  Google Scholar 

  20. S.N. Solodukhin, Living Rev. Relativ. 14, 8 (2011) arXiv:1104.3712.

    Article  ADS  Google Scholar 

  21. S.N. Solodukhin, Phys. Rev. D 51, 618 (1995) arXiv:hep-th/9408068.

    Article  MathSciNet  ADS  Google Scholar 

  22. S.N. Solodukhin, Phys. Rev. D 51, 609 (1995) arXiv:hep-th/9407001.

    Article  MathSciNet  ADS  Google Scholar 

  23. R.B. Mann, S.N. Solodukhin, Nucl. Phys. B 523, 293 (1998) arXiv:hep-th/9709064.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  24. R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki, Rev. Mod. Phys. 81, 865 (2009).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  25. J. Eisert, M. Cramer, M.B. Plenio, Rev. Mod. Phys. 82, 277 (2010) arXiv:0808.3773.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  26. S. Das, S. Shankaranarayanan, S. Sur, Phys. Rev. D 77, 064013 (2008) arXiv:0705.2070.

    Article  ADS  Google Scholar 

  27. D.N. Kabat, M.J. Strassler, Phys. Lett. B 329, 46 (1994).

    Article  ADS  Google Scholar 

  28. D.N. Kabat, Nucl. Phys. B 453, 281 (1995).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  29. C. Holzhey, F. Larsen, F. Wilczek, Nucl. Phys. B 424, 443 (1994) hep-th/9403108.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. C. Callan, F. Wilczek, Phys. Lett. B 333, 55 (1994).

    Article  MathSciNet  ADS  Google Scholar 

  31. P. Calabrese, J. Cardy, Stat. Mech. 06, P002 (2004) arXiv:hep-th/0405152.

    MathSciNet  Google Scholar 

  32. G. Vidal, J.I. Latorre, E. Rico, A. Kitaev, Phys. Rev. Lett. 90, 227902 (2003) quant-ph/0211074.

    Article  ADS  Google Scholar 

  33. J.I. Latorre, E. Rico, G. Vidal, Quantum. Inf. Comput. 4, 048 (2004) quant-ph/0304098.

    MathSciNet  Google Scholar 

  34. H. Casini, M. Huerta, Nucl. Phys. B 764, 183 (2007).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  35. H. Casini, M. Huerta, Phys. Lett. B 694, 167 (2010).

    Article  MathSciNet  ADS  Google Scholar 

  36. S. Ryu, T. Takayanagi, Phys. Rev. Lett. 96, 181602 (2006) arXiv:hep-th/0603001.

    Article  MathSciNet  ADS  Google Scholar 

  37. S. Ryu, T. Takayanagi, JHEP 08, 045 (2006) hep-th/0605073.

    Article  MathSciNet  ADS  Google Scholar 

  38. H. Casini, M. Huerta, R.C. Myers, JHEP 05, 036 (2011).

    Article  MathSciNet  ADS  Google Scholar 

  39. A. Lewkowycz, J. Maldacena, JHEP 08, 090 (2013) arXiv:1304.4926 [hep-th].

    Article  MathSciNet  ADS  Google Scholar 

  40. M.B. Plenio, J. Eisert, J. Dreissig, M. Cramer, Phys. Rev. Lett. 94, 060503 (2005) quant-ph/0405142.

    Article  MathSciNet  ADS  Google Scholar 

  41. I. Peschel, V. Eisler, J. Phys. A: Math. Theor. 42, 504003 (2009).

    Article  MathSciNet  Google Scholar 

  42. R.M. Wald, Living Rev. Relativ. 4, 6 (2001) gr-qc/9912119.

    Article  ADS  Google Scholar 

  43. S.L. Braunstein, S. Das, S. Shankaranarayanan, JHEP 07, 130 (2013) hep-th/1110.1239.

    Article  MathSciNet  ADS  Google Scholar 

  44. K. Mallayya, R. Tibrewala, S. Shankaranarayanan, T. Padmanabhan, Phys. Rev. D 90, 044058 (2014) arXiv:1404.2079 [hep-th].

    Article  ADS  Google Scholar 

  45. H. Casini, M. Huerta, J. Phys. A 42, 504007 (2009) arXiv:0905.2562 [hep-th].

    Article  MathSciNet  Google Scholar 

  46. S. Das, S. Shankaranarayanan, S. Sur, Black hole entropy from entanglement: A Review, gr-qc/0806.0402.

  47. S.S. Kumar, S. Ghosh, S. Shankaranarayanan, Phys. Rev. D 89, 065019 (2014) arXiv:1401.2839 [hep-th].

    Article  ADS  Google Scholar 

  48. R. Emparan, H.S. Reall, Phys. Rev. Lett. 88, 101101 (2002) hep-th/0110260.

    Article  MathSciNet  ADS  Google Scholar 

  49. R. Emparan, H.S. Reall, Class. Quantum. Grav. 23, R169 (2006) hep-th/0608012.

    Article  MathSciNet  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Suman Ghosh.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ghosh, S. Entanglement entropy due to near-horizon degrees of freedom. Eur. Phys. J. Plus 130, 154 (2015). https://doi.org/10.1140/epjp/i2015-15154-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2015-15154-9

Keywords

Navigation