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Journal of High Energy Physics

, 2010:119 | Cite as

The curious case of null warped space

  • Dionysios Anninos
  • Geoffrey Compère
  • Sophie de Buyl
  • Stéphane Detournay
  • Monica Guica
Open Access
Article

Abstract

We initiate a comprehensive study of a set of solutions of topologically massive gravity known as null warped anti-de Sitter spacetimes. These are pp-wave extensions of three-dimensional anti-de Sitter space. We first perform a careful analysis of the linearized stability of black holes in these spacetimes. We find two qualitatively different types of solutions to the linearized equations of motion: the first set has an exponential time dependence, the second — a polynomial time dependence. The solutions polynomial in time induce severe pathologies and moreover survive at the non-linear level. In order to make sense of these geometries, it is thus crucial to impose appropriate boundary conditions. We argue that there exists a consistent set of boundary conditions that allows us to reject the above pathological modes from the physical spectrum. The asymptotic symmetry group associated to these boundary conditions consists of a centrally-extended Virasoro algebra. Using this central charge we can account for the entropy of the black holes via Cardy’s formula. Finally, we note that the black hole spectrum is chiral and prove a Birkoff theorem showing that there are no other stationary axisymmetric black holes with the specified asymptotics. We extend most of the analysis to a larger family of pp-wave black holes which are related to Schrödinger spacetimes with critical exponent z.

Keywords

Gauge-gravity correspondence Models of Quantum Gravity Black Holes 

References

  1. [1]
    E. Witten, Three-dimensional gravity revisited, arXiv:0706.3359 [SPIRES].
  2. [2]
    A. Maloney and E. Witten, Quantum gravity partition functions in three dimensions, JHEP 02 (2010) 029 [arXiv:0712.0155] [SPIRES].CrossRefADSGoogle Scholar
  3. [3]
    W. Li, W. Song and A. Strominger, Chiral gravity in three dimensions, JHEP 04 (2008) 082 [arXiv:0801.4566] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  4. [4]
    A. Maloney, W. Song and A. Strominger, Chiral gravity, log gravity and extremal CFT, Phys. Rev. D 81 (2010) 064007 [arXiv:0903.4573] [SPIRES].ADSGoogle Scholar
  5. [5]
    D. Grumiller and N. Johansson, Instability in cosmological topologically massive gravity at the chiral point, JHEP 07 (2008) 134 [arXiv:0805.2610] [SPIRES].CrossRefADSGoogle Scholar
  6. [6]
    D. Grumiller and N. Johansson, Erratum to: Instability in cosmological topologically massive gravity at the chiral point, arXiv:0910.1706 [SPIRES].
  7. [7]
    K. Skenderis, M. Taylor and B.C. van Rees, Topologically massive gravity and the AdS/CFT correspondence, JHEP 09 (2009) 045 [arXiv:0906.4926] [SPIRES].CrossRefADSGoogle Scholar
  8. [8]
    D. Grumiller and I. Sachs, A dS 3 /LCFT 2 — correlators in cosmological topologically massive gravity, JHEP 03 (2010) 012 [arXiv:0910.5241] [SPIRES].CrossRefADSGoogle Scholar
  9. [9]
    S. Deser, R. Jackiw and S. Templeton, Topologically massive gauge theories, Ann. Phys. 140 (1982) 372 [Erratum ibid. 185 (1988) 406] [Ann. Phys. 185 (1988) 406] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  10. [10]
    J.D. Brown and M. Henneaux, Central charges in the canonical realization of asymptotic symmetries: an example from three-dimensional gravity, Commun. Math. Phys. 104 (1986) 207 [SPIRES].zbMATHCrossRefMathSciNetADSGoogle Scholar
  11. [11]
    G. Compere and S. Detournay, Semi-classical central charge in topologically massive gravity, Class. Quant. Grav. 26 (2009) 012001 [Erratum ibid. 26 (2009) 139801] [arXiv:0808.1911] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  12. [12]
    G. Compere and S. Detournay, Boundary conditions for spacelike and timelike warped AdS 3 spaces in topologically massive gravity, JHEP 08 (2009) 092 [arXiv:0906.1243] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  13. [13]
    M. Blagojevic and B. Cvetkovic, Asymptotic structure of topologically massive gravity in spacelike stretched AdS sector, JHEP 09 (2009) 006 [arXiv:0907.0950] [SPIRES].CrossRefADSGoogle Scholar
  14. [14]
    D.T. Son, Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry, Phys. Rev. D 78 (2008) 046003 [arXiv:0804.3972] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  15. [15]
    K. Balasubramanian and J. McGreevy, Gravity duals for non-relativistic CFTs, Phys. Rev. Lett. 101 (2008) 061601 [arXiv:0804.4053] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  16. [16]
    M. Guica, T. Hartman, W. Song and A. Strominger, The Kerr/CFT correspondence, Phys. Rev. D 80 (2009) 124008 [arXiv:0809.4266] [SPIRES].ADSGoogle Scholar
  17. [17]
    G. Clement, Particle — like solutions to topologically massive gravity, Class. Quant. Grav. 11 (1994) L115 [gr-qc/9404004] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  18. [18]
    A. Bouchareb and G. Clement, Black hole mass and angular momentum in topologically massive gravity, Class. Quant. Grav. 24 (2007) 5581 [arXiv:0706.0263] [SPIRES].zbMATHCrossRefMathSciNetADSGoogle Scholar
  19. [19]
    S. Deser, R. Jackiw and S. Templeton, Three-dimensional massive gauge theories, Phys. Rev. Lett. 48 (1982) 975 [SPIRES].CrossRefADSGoogle Scholar
  20. [20]
    Y. Nutku, Exact solutions of topologically massive gravity with a cosmological constant, Class. Quant. Grav. 10 (1993) 2657 [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  21. [21]
    M. Gurses, Gódel type metrics in three dimensions, arXiv:0812.2576 [SPIRES].
  22. [22]
    D. Anninos, W. Li, M. Padi, W. Song and A. Strominger, Warped AdS 3 black holes, JHEP 03 (2009) 130 [arXiv:0807.3040] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  23. [23]
    D.D.K. Chow, C.N. Pope and E. Sezgin, Classification of solutions in topologically massive gravity, Class. Quant. Grav. 27 (2010) 105001 [arXiv:0906.3559] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  24. [24]
    D. Anninos, Sailing from warped AdS 3 to warped dS 3 in topologically massive gravity, JHEP 02 (2010) 046 [arXiv:0906.1819] [SPIRES].CrossRefADSGoogle Scholar
  25. [25]
    S. Deser, R. Jackiw and S.Y. Pi, Cotton blend gravity pp waves, Acta Phys. Polon. B 36 (2005) 27 [gr-qc/0409011] [SPIRES].MathSciNetADSGoogle Scholar
  26. [26]
    G.W. Gibbons, C.N. Pope and E. Sezgin, The general supersymmetric solution of topologically massive supergravity, Class. Quant. Grav. 25 (2008) 205005 [arXiv:0807.2613] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  27. [27]
    K. Hotta, Y. Hyakutake, T. Kubota and H. Tanida, Brown-Henneaux’s canonical approach to topologically massive gravity, JHEP 07 (2008) 066 [arXiv:0805.2005] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  28. [28]
    M. Henneaux, C. Martinez and R. Troncoso, Asymptotically anti-de Sitter spacetimes in topologically massive gravity, Phys. Rev. D 79 (2009) 081502 [arXiv:0901.2874] [SPIRES].MathSciNetADSGoogle Scholar
  29. [29]
    M. Blau, J. Hartong and B. Rollier, Geometry of Schroedinger space-times, global coordinates and harmonic trapping, JHEP 07 (2009) 027 [arXiv:0904.3304] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  30. [30]
    W. Boucher, G.W. Gibbons and G.T. Horowitz, A uniqueness theorem for anti-de Sitter space-time, Phys. Rev. D 30 (1984) 2447 [SPIRES].MathSciNetADSGoogle Scholar
  31. [31]
    O. Coussaert and M. Henneaux, Self-dual solutions of (2+1) Einstein gravity with a negative cosmological constant, hep-th/9407181 [SPIRES].
  32. [32]
    V. Pravda, A. Pravdova, A. Coley and R. Milson, All spacetimes with vanishing curvature invariants, Class. Quant. Grav. 19 (2002) 6213 [gr-qc/0209024] [SPIRES].zbMATHCrossRefMathSciNetADSGoogle Scholar
  33. [33]
    A. Coley, S. Hervik and N. Pelavas, Spacetimes characterized by their scalar curvature invariants, Class. Quant. Grav. 26 (2009) 025013 [arXiv:0901.0791] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  34. [34]
    A. Coley, S. Hervik and N. Pelavas, Lorentzian spacetimes with constant curvature invariants in three dimensions, Class. Quant. Grav. 25 (2008) 025008 [arXiv:0710.3903] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  35. [35]
    A. Coley, S. Hervik and N. Pelavas, Lorentzian manifolds and scalar curvature invariants, Class. Quant. Grav. 27 (2010) 102001 [arXiv:1003.2373] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  36. [36]
    A. Coley, S. Hervik, G.O. Papadopoulos and N. Pelavas, Kundt spacetimes, Class. Quant. Grav. 26 (2009) 105016 [arXiv:0901.0394][SPIRES].CrossRefMathSciNetADSGoogle Scholar
  37. [37]
    A. Ishibashi and R.M. Wald, Dynamics in non-globally hyperbolic static spacetimes. III: anti-de Sitter spacetime, Class. Quant. Grav. 21 (2004) 2981 [hep-th/0402184] [SPIRES].zbMATHCrossRefMathSciNetADSGoogle Scholar
  38. [38]
    J. Lee and R.M. Wald, Local symmetries and constraints, J. Math. Phys. 31 (1990) 725 [SPIRES].zbMATHCrossRefMathSciNetADSGoogle Scholar
  39. [39]
    S. Deser and B. Tekin, Massive, topologically massive, models, Class. Quant. Grav. 19 (2002) L97 [hep-th/0203273] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  40. [40]
    S. Carlip, S. Deser, A. Waldron and D.K. Wise, Cosmological topologically massive gravitons and photons, Class. Quant. Grav. 26 (2009) 075008 [arXiv:0803.3998] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  41. [41]
    W.H. Press and S.A. Teukolsky, Floating orbits, superradiant scattering and the black-hole bomb, Nature 238 (1972) 211 [SPIRES].CrossRefADSGoogle Scholar
  42. [42]
    V. Cardoso, O.J.C. Dias, J.P.S. Lemos and S. Yoshida, The black hole bomb and superradiant instabilities, Phys. Rev. D 70 (2004) 044039 [Erratum ibid. D 70 (2004) 049903] [hep-th/0404096] [SPIRES].MathSciNetADSGoogle Scholar
  43. [43]
    B.S. Kay, M.J. Radzikowski and R.M. Wald, Quantum field theory on spacetimes with a compactly generated Cauchy horizon, Commun. Math. Phys. 183 (1997) 533 [gr-qc/9603012] [SPIRES].zbMATHCrossRefMathSciNetADSGoogle Scholar
  44. [44]
    D. Birmingham, I. Sachs and S.N. Solodukhin, Conformal field theory interpretation of black hole quasi-normal modes, Phys. Rev. Lett. 88 (2002) 151301 [hep-th/0112055] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  45. [45]
    T. Hartman, W. Song and A. Strominger, Holographic derivation of Kerr-Newman scattering amplitudes for general charge and spin, JHEP 03 (2010) 118 [arXiv:0908.3909] [SPIRES].CrossRefADSGoogle Scholar
  46. [46]
    B. Chen and Z.-b. Xu, Quasi-normal modes of warped black holes and warped AdS/CFT correspondence, JHEP 11 (2009) 091 [arXiv:0908.0057] [SPIRES].CrossRefADSGoogle Scholar
  47. [47]
    B. Chen, B. Ning and Z.-b. Xu, Real-time correlators in warped AdS/CFT correspondence, JHEP 02 (2010) 031 [arXiv:0911.0167] [SPIRES].CrossRefADSGoogle Scholar
  48. [48]
    B. Chen and C.-S. Chu, Real-time correlators in Kerr/CFT correspondence, JHEP 05 (2010) 004 [arXiv:1001.3208] [SPIRES].CrossRefADSGoogle Scholar
  49. [49]
    D. Anninos and T. Anous, A de Sitter Hoedown, JHEP 08 (2010) 131 [arXiv:1002.1717] [SPIRES].CrossRefADSGoogle Scholar
  50. [50]
    G. Compere and D. Marolf, Setting the boundary free in AdS/CFT, Class. Quant. Grav. 25 (2008) 195014 [arXiv:0805.1902] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  51. [51]
    G. Barnich and F. Brandt, Covariant theory of asymptotic symmetries, conservation laws and central charges, Nucl. Phys. B 633 (2002) 3 [hep-th/0111246] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  52. [52]
    G. Barnich and G. Compere, Surface charge algebra in gauge theories and thermodynamic integrability, J. Math. Phys. 49 (2008) 042901 [arXiv:0708.2378] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  53. [53]
    D. Anninos, M. Esole and M. Guica, Stability of warped AdS3 vacua of topologically massive gravity, JHEP 10 (2009) 083 [arXiv:0905.2612] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  54. [54]
    Y.-W. Kim, Y.S. Myung and Y.-J. Park, Nonpropagation of massive mode on AdS2 in topologically massive gravity, Eur. Phys. J. C 67 (2010) 533 [arXiv:0901.4390] [SPIRES].CrossRefADSGoogle Scholar
  55. [55]
    A. Strominger, A simple proof of the chiral gravity conjecture, arXiv:0808.0506 [SPIRES].
  56. [56]
    G. Barnich and G. Compere, Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions, Class. Quant. Grav. 24 (2007) F15 [gr-qc/0610130] [SPIRES].zbMATHCrossRefMathSciNetADSGoogle Scholar
  57. [57]
    G. Compere, Symmetries and conservation laws in Lagrangian gauge theories with applications to the mechanics of black holes and to gravity in three dimensions, arXiv:0708.3153 [SPIRES].
  58. [58]
    R.M. Wald and A. Zoupas, A general definition of ”Conserved Quantities” in general relativity and other theories of gravity, Phys. Rev. D 61 (2000) 084027 [gr-qc/9911095] [SPIRES].MathSciNetADSGoogle Scholar
  59. [59]
    T. Andrade and D. Marolf, No chiral truncation of quantum log gravity?, JHEP 03 (2010) 029 [arXiv:0909.0727] [SPIRES].CrossRefADSGoogle Scholar
  60. [60]
    P. Hořava and C.M. Melby-Thompson, Anisotropic conformal infinity, arXiv:0909.3841 [SPIRES].

Copyright information

© The Author(s) 2010

Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  • Dionysios Anninos
    • 1
  • Geoffrey Compère
    • 2
  • Sophie de Buyl
    • 2
  • Stéphane Detournay
    • 3
  • Monica Guica
    • 4
  1. 1.Center for the Fundamental Laws of NatureHarvard UniversityCambridgeU.S.A.
  2. 2.Department of PhysicsUniversity of CaliforniaSanta BarbaraU.S.A.
  3. 3.Kavli Institute for Theoretical PhysicsUniversity of CaliforniaSanta BarbaraU.S.A.
  4. 4.Laboratoire de Physique Théorique et Hautes Energies(LPTHE)Paris Cedex 05France

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