Advertisement

Determining an asymptotically AdS Einstein spacetime from data on its conformal boundary

  • Alberto EncisoEmail author
  • Niky Kamran
Research Article

Abstract

An outstanding question lying at the core of the AdS/CFT correspondence in string theory is the holographic prescription problem for Einstein metrics, which asserts that one can slightly perturb the conformal geometry at infinity of the anti-de Sitter space and still obtain an asymptotically anti-de Sitter spacetime that satisfies the Einstein equations with a negative cosmological constant. The purpose of this paper is to address this question by providing a precise quantitative statement of the real-time holographic principle for Einstein spacetimes, to outline its proof and to discuss its physical implications.

Keywords

AdS metrics Holographic prescription Einstein equations AdS/CFT correspondence 

Notes

Acknowledgments

A.E. is supported by the ERC Starting Grant 633152 and thanks McGill University for hospitality and support. A.E.’s research is supported in part by the ICMAT Severo Ochoa Grant SEV-2011-0087 and the MINECO Grant FIS2011-22566. The research of N.K. is supported by NSERC Grant RGPIN 105490-2011.

References

  1. 1.
    Enciso, A., Kamran, N.: Lorentzian Einstein metrics with prescribed conformal infinity. arXiv:1412.4376
  2. 2.
    Maldacena, J.: Adv. Theor. Math. Phys. 2, 231 (1998)zbMATHMathSciNetADSGoogle Scholar
  3. 3.
    Witten, E.: Adv. Theor. Math. Phys. 2, 253 (1998)zbMATHMathSciNetADSGoogle Scholar
  4. 4.
    Balasubramanian, V., Kraus, P.: Commun. Math. Phys. 208, 413 (1999)zbMATHMathSciNetCrossRefADSGoogle Scholar
  5. 5.
    Son, D.T., Starinets, A.O.: JHEP 09, 042 (2002)MathSciNetCrossRefADSGoogle Scholar
  6. 6.
    de Haro, S., Solodukhin, S.N., Skenderis, K.: Commun. Math. Phys. 217, 595 (2001)zbMATHCrossRefADSGoogle Scholar
  7. 7.
    Bianchi, M., Freedman, D.Z., Skenderis, K.: Nucl. Phys. B 631, 159 (2002)zbMATHMathSciNetCrossRefADSGoogle Scholar
  8. 8.
    Graham, C.R., Lee, J.M.: Adv. Math. 87, 186 (1991)zbMATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    Fefferman, C., Graham, C.R.: The Ambient Metric. Princeton University Press, Princeton (2012)zbMATHGoogle Scholar
  10. 10.
    Breitenlohner, P., Freedman, D.Z.: Ann. Phys. 144, 249 (1982)zbMATHMathSciNetCrossRefADSGoogle Scholar
  11. 11.
    Choquet-Bruhat, Y.: Class. Quant. Gravity 6, 1781 (1989)zbMATHMathSciNetCrossRefADSGoogle Scholar
  12. 12.
    Ishibashi, A., Wald, R.M.: Class. Quant. Gravity 21, 2981 (2004)zbMATHMathSciNetCrossRefADSGoogle Scholar
  13. 13.
    Bachelot, A.: J. Math. Pures Appl. 96, 527 (2011)zbMATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    Enciso, A., Kamran, N.: Phys. Rev. D 85, 106016 (2012)CrossRefADSGoogle Scholar
  15. 15.
    Bachelot, A.: Commun. Math. Phys. 320, 723 (2013)zbMATHMathSciNetCrossRefADSGoogle Scholar
  16. 16.
    Vasy, A.: Anal. PDE 5, 81 (2012)zbMATHMathSciNetCrossRefGoogle Scholar
  17. 17.
    Holzegel, G.: J. Hyperb. Differ. Equ. 9, 239 (2012)zbMATHMathSciNetCrossRefGoogle Scholar
  18. 18.
    Warnick, C.: Commun. Math. Phys. 321, 85 (2013)zbMATHMathSciNetCrossRefADSGoogle Scholar
  19. 19.
    Holzegel, G., Warnick, C.: J. Funct. Anal. 266, 2436 (2014)zbMATHMathSciNetCrossRefGoogle Scholar
  20. 20.
    Enciso, A., Kamran, N.: J. Math. Pures Appl. 103, 1053 (2015)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Friedrich, H.: J. Geom. Phys. 17, 125–184 (1995)zbMATHMathSciNetCrossRefADSGoogle Scholar
  22. 22.
    DeTurck, D.M.: Compos. Math. 48, 327 (1983)zbMATHMathSciNetADSGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Instituto de Ciencias MatemáticasConsejo Superior de Investigaciones CientíficasMadridSpain
  2. 2.Department of Mathematics and StatisticsMcGill UniversityMontrealCanada

Personalised recommendations