Skip to main content
SpringerLink
Log in

Quasilocal energy for three-dimensional massive gravity solutions with chiral deformations of AdS\(_3\) boundary conditions

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

Abstract

We consider critical gravity in three dimensions; that is, the New Massive Gravity theory formulated about Anti-de Sitter (AdS) space with the specific value of the graviton mass for which it results dual to a two-dimensional conformal field theory with vanishing central charge. As it happens with Kerr black holes in four-dimensional critical gravity, in three-dimensional critical gravity the Bañados–Teitelboim–Zanelli black holes have vanishing mass and vanishing angular momentum. However, provided suitable asymptotic conditions are chosen, the theory may also admit solutions carrying non-vanishing charges. Here, we give simple examples of exact solutions that exhibit falling-off conditions that are even weaker than those of the so-called Log-gravity. For such solutions, we define the quasilocal stress-tensor and use it to compute conserved charges. Despite the drastic deformation of AdS\(_3\) asymptotic, these solutions have non-zero mass and angular momentum, which we compute.

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

References

  1. Bergshoeff, E., Hohm, O., Townsend, P.: Phys. Rev. Lett. 102, 201301 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  2. Bergshoeff, E., Hohm, O., Townsend, P.: Phys. Rev. D79, 124042 (2009)

    ADS  MathSciNet  Google Scholar 

  3. Deser, S., Jackiw, R., Tempelton, S.: Ann. Phys. 140, 372 (1982)

    Article  ADS  Google Scholar 

  4. Deser, S., Jackiw, R., Tempelton, S.: Phys. Rev. Lett. 48, 975 (1982)

    Article  ADS  Google Scholar 

  5. Grumiller, D., Hohm, O.: Phys. Lett. B686, 2640905 (2010)

    MathSciNet  Google Scholar 

  6. Grumiller, D., Johansson, N.: JHEP 0807, 134 (2008)

    Article  ADS  Google Scholar 

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

    Article  ADS  MATH  MathSciNet  Google Scholar 

  8. Maldacena, J.M.: Adv. Theory Math. Phys. 2, 231 (1998)

    ADS  MATH  MathSciNet  Google Scholar 

  9. Li, W., Song, W., Strominger, A.: JHEP 0804, 082 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  10. Carlip, S., Deser, S., Waldron, A., Wise, D.: Phys. Lett. B666, 272 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  11. Carlip, S., Deser, S., Waldron, A., Wise, D.: Class. Quantum Gravity 26, 075008 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  12. Giribet, G., Kleban, M., Porrati, M.: JHEP 0810, 045 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  13. Maloney, A., Song, W., Strominger, A.: Phys. Rev. D81, 064007 (2010)

    ADS  MathSciNet  Google Scholar 

  14. Grumiller, D., Johansson, N.: Int. J. Mod. Phys. D17, 2367 (2009)

    ADS  MathSciNet  Google Scholar 

  15. Henneaux, M., Martínez, C., Troncoso, R.: Phys. Rev. D82, 064038 (2010)

    ADS  Google Scholar 

  16. Henneaux, M., Martínez, C., Troncoso, R., Zanelli, J.: Phys. Rev. D65, 104007 (2002)

    ADS  Google Scholar 

  17. Oliva, J., Tempo, D., Troncoso, R.: JHEP 0907, 011 (2009)

    Article  ADS  Google Scholar 

  18. Henneaux, M., Martínez, C., Troncoso, R.: Phys. Rev. D79, 081502R (2009)

    ADS  Google Scholar 

  19. Liu, Y., Sun, Y.-W.: JHEP 0904, 106 (2009)

    Article  ADS  Google Scholar 

  20. Liu, Y., Sun, Y.-W.: JHEP 0905, 039 (2009)

    Article  ADS  Google Scholar 

  21. Liu, Y., Sun, Y.-W.: Phys. Rev. D79, 126001 (2009)

    ADS  Google Scholar 

  22. Compère, G., Song, W., Strominger, A.: arXiv:1303.2662

  23. Brown, J., York, J.: Phys. Rev. D47, 1407 (1993)

    ADS  MathSciNet  Google Scholar 

  24. Hohm, O., Tonni, E.: JHEP 1004, 093 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  25. Giribet, G., Leston, M.: JHEP 1009, 070 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  26. Giribet, G., Goya, A., Leston, M.: Phys. Rev. D84, 066003 (2011)

    ADS  Google Scholar 

  27. Correa, F., Martínez, C., Troncoso, R.: JHEP 1202, 136 (2012)

    Article  ADS  Google Scholar 

  28. Giribet, G., Goya, A.: JHEP 1303, 130 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  29. Bañados, M., Teitelboim, C., Zanelli, J.: Phys. Rev. Lett. 69, 1849 (1992)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  30. Bañados, M., Henneaux, M., Teitelboim, C., Zanelli, J.: Phys. Rev. D48, 1506 (1993)

    ADS  Google Scholar 

  31. Gibbons, G., Pope, C., Sezgin, E.: Class. Quantum Gravity 25, 205005 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  32. Garbarz, A., Giribet, G., Vásquez, Y.: Phys. Rev. D79, 044036 (2009)

    ADS  Google Scholar 

  33. Clément, G.: Class. Quantum Gravity 26, 165002 (2009)

    Article  ADS  Google Scholar 

  34. Bergshoeff, E., Fernández-Melgarejo, J., Rosseel, J., Townsend, P.: JHEP 1204, 070 (2012)

    Article  ADS  Google Scholar 

  35. Ayón-Beato, E., Giribet, G., Hassaïne, M.: JHEP 0905, 029 (2009)

    Article  ADS  Google Scholar 

  36. Fefferman, C., Graham, C.: Conformal invariants, in Elie Cartan et les Mathématiques d’aujourd’hui (Asterisque) 95 (1985).

  37. Cunliff, C.: JHEP 1304, 141 (2013)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Acknowledgments

This work has been supported by UBA, CONICET, and ANPCyT. The authors are grateful to Stéphane Detournay and Guillem Pérez–Nadal for discussions. G.G. thanks Pontificia Universidad Católica de Valparaíso for the hospitality during his stays, where part of this work was done.

Author information

Authors and Affiliations

  1. Departamento de Física, Universidad de Buenos Aires FCEN-UBA, IFIBA-CONICET, Ciudad Universitaria, Pabellón I, 1428 , Buenos Aires, Argentina

    Alan Garbarz, Gaston Giribet & Andrés Goya

  2. Instituto de Física de La Plata, Universidad Nacional de La Plata IFLP-UNLP, C.C. 67, 1900 , La Plata, Argentina

    Alan Garbarz

  3. Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla , 4950, Valparaiso, Chile

    Gaston Giribet

  4. Instituto de Astronomía y Física del Espacio IAFE-CONICET, Ciudad Universitaria, C.C. 67 Suc. 28, 1428 , Buenos Aires, Argentina

    Mauricio Leston

Authors
  1. Alan Garbarz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gaston Giribet
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Andrés Goya
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mauricio Leston
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gaston Giribet.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Garbarz, A., Giribet, G., Goya, A. et al. Quasilocal energy for three-dimensional massive gravity solutions with chiral deformations of AdS\(_3\) boundary conditions. Gen Relativ Gravit 46, 1735 (2014). https://doi.org/10.1007/s10714-014-1735-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10714-014-1735-x

Keywords

Search

Navigation