Advertisement

Anti de Sitter black holes and branes in dynamical Chern-Simons gravity: perturbations, stability and the hydrodynamic modes

  • Térence Delsate
  • Vitor Cardoso
  • Paolo Pani
Article

Abstract

Dynamical Chern-Simons (DCS) theory is an extension of General Relativity in which the gravitational field is coupled to a scalar field through a parity violating term. We study perturbations of anti-de Sitter black holes and branes in such a theory, and show that the relevant equations reduce to a set of coupled ODEs which can be solved efficiently through a series expansion. We prove numerically that black holes and branes in DCS gravity are stable against gravitational and scalar perturbations in the entire parameter space. Furthermore, by applying the AdS/CFT duality, were late black hole perturbations to hydrodynamic quantities in the dual field theory, which is a (2 + 1)-dimensional isotropic fluid with broken spatial parity. The Chern-Simons term does not affect the entropy to viscosity ratio and the relaxation time, but instead quantities that enter the shear mode at order q 4 in the small momentum limit, for example the Hall viscosity and other quantities related to second and third order hydrodynamics. We provide explicit corrections to the gravitational hydrodynamic mode to first relevant order in the couplings.

Keywords

AdS-CFT Correspondence Chern-Simons Theories Black Holes 

References

  1. [1]
    S. Deser, R. Jackiw and S. Templeton, Three-Dimensional Massive Gauge Theories, Phys. Rev. Lett. 48 (1982) 975 [SPIRES].ADSCrossRefGoogle Scholar
  2. [2]
    A. Lue, L.-M. Wang and M. Kamionkowski, Cosmological signature of new parity-violating interactions, Phys. Rev. Lett. 83 (1999) 1506 [astro-ph/9812088] [SPIRES].ADSCrossRefGoogle Scholar
  3. [3]
    R. Jackiw and S.Y. Pi, Chern-Simons modification of general relativity, Phys. Rev. D 68 (2003) 104012 [gr-qc/0308071] [SPIRES].MathSciNetADSGoogle Scholar
  4. [4]
    S. Alexander and N. Yunes, Chern-Simons Modified General Relativity, Phys. Rept. 480 (2009) 1 [arXiv:0907.2562] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    S. Weinberg, A Tree Theorem for Inflation, Phys. Rev. D 78 (2008) 063534 [arXiv:0805.3781] [SPIRES].MathSciNetADSGoogle Scholar
  6. [6]
    S.H.-S. Alexander, M.E. Peskin and M.M. Sheikh-Jabbari, Leptogenesis from gravity waves in models of inflation, Phys. Rev. Lett. 96 (2006) 081301 [hep-th/0403069] [SPIRES].ADSCrossRefGoogle Scholar
  7. [7]
    J. García-Bellido, M. Garcia-Perez and A. Gonzalez-Arroyo, Chern-Simons production during preheating in hybrid inflation models, Phys. Rev. D 69 (2004) 023504 [hep-ph/0304285] [SPIRES].ADSGoogle Scholar
  8. [8]
    S.H.S. Alexander and S.J. Gates, Jr., Can the string scale be related to the cosmic baryon asymmetry?, JCAP 06 (2006) 018 [hep-th/0409014] [SPIRES].ADSGoogle Scholar
  9. [9]
    J. Polchinski, String theory. Vol. 2: Superstring theory and beyond, Cambridge Univ. Pr., Cambridge U.K. (1998).CrossRefGoogle Scholar
  10. [10]
    A. Ashtekar, A.P. Balachandran and S. Jo, The CP problem in quantum gravity, Int. J. Mod. Phys. A4 (1989) 1493 [SPIRES].MathSciNetADSGoogle Scholar
  11. [11]
    V. Taveras and N. Yunes, The Barbero-Immirzi Parameter as a Scalar Field: K-Inflation from Loop Quantum Gravity?, Phys. Rev. D 78 (2008) 064070 [arXiv:0807.2652] [SPIRES].MathSciNetADSGoogle Scholar
  12. [12]
    S. Mercuri and V. Taveras, Interaction of the Barbero–Immirzi Field with Matter and Pseudo-Scalar Perturbations, Phys. Rev. D 80 (2009) 104007 [arXiv:0903.4407] [SPIRES].MathSciNetADSGoogle Scholar
  13. [13]
    E. Barausse and T.P. Sotiriou, Perturbed Kerr Black Holes can probe deviations from General Relativity, Phys. Rev. Lett. 101 (2008) 099001 [arXiv:0803.3433] [SPIRES].ADSCrossRefGoogle Scholar
  14. [14]
    E. Berti, V. Cardoso and A.O. Starinets, Quasinormal modes of black holes and black branes, Class. Quant. Grav. 26 (2009) 163001 [arXiv:0905.2975] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  15. [15]
    V. Cardoso and L. Gualtieri, Perturbations of Schwarzschild black holes in Dynamical Chern-Simons modified gravity, Phys. Rev. D 80 (2009) 064008 [arXiv:0907.5008] [SPIRES].ADSGoogle Scholar
  16. [16]
    C. Molina, P. Pani, V. Cardoso and L. Gualtieri, Gravitational signature of Schwarzschild black holes in dynamical Chern-Simons gravity, Phys. Rev. D 81 (2010) 124021 [arXiv:1004.4007] [SPIRES].ADSGoogle Scholar
  17. [17]
    H. Ahmedov and A.N. Aliev, Black String and Gódel type Solutions of Chern-Simons Modified Gravity, Phys. Rev. D 82 (2010) 024043 [arXiv:1003.6017] [SPIRES].MathSciNetADSGoogle Scholar
  18. [18]
    O. Saremi and D.T. Son, Hall viscosity from gauge/gravity duality, arXiv:1103.4851 [SPIRES].
  19. [19]
    J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [SPIRES].MathSciNetMATHCrossRefGoogle Scholar
  20. [20]
    P.K. Kovtun and A.O. Starinets, Quasinormal modes and holography, Phys. Rev. D 72 (2005) 086009 [hep-th/0506184] [SPIRES].ADSGoogle Scholar
  21. [21]
    P. Kovtun, D.T. Son and A.O. Starinets, Viscosity in strongly interacting quantum field theories from black hole physics, Phys. Rev. Lett. 94 (2005) 111601 [hep-th/0405231] [SPIRES].ADSCrossRefGoogle Scholar
  22. [22]
    S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear Fluid Dynamics from Gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [SPIRES].ADSCrossRefGoogle Scholar
  23. [23]
    J. Erdmenger, M. Haack, M. Kaminski and A. Yarom, Fluid dynamics of R-charged black holes, JHEP 01 (2009) 055 [arXiv:0809.2488] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  24. [24]
    J.P.S. Lemos, Cylindrical black hole in general relativity, Phys. Lett. B 353 (1995) 46 [gr-qc/9404041] [SPIRES].MathSciNetADSGoogle Scholar
  25. [25]
    T. Torii, K. Maeda and M. Narita, Scalar hair on the black hole in asymptotically anti-de Sitter spacetime, Phys. Rev. D 64 (2001) 044007 [SPIRES].MathSciNetADSGoogle Scholar
  26. [26]
    A.S. Miranda, J. Morgan and V.T. Zanchin, Quasinormal modes of plane-symmetric black holes according to the AdS/CFT correspondence, JHEP 11 (2008) 030 [arXiv:0809.0297] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  27. [27]
    J. Morgan, V. Cardoso, A.S. Miranda, C. Molina and V.T. Zanchin, Gravitational quasinormal modes of AdS black branes in d spacetime dimensions, JHEP 09 (2009) 117 [arXiv:0907.5011] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  28. [28]
    G.T. Horowitz and V.E. Hubeny, Quasinormal modes of AdS black holes and the approach to thermal equilibrium, Phys. Rev. D 62 (2000) 024027 [hep-th/9909056] [SPIRES].MathSciNetADSGoogle Scholar
  29. [29]
    V. Cardoso and J.P.S. Lemos, Quasi-normal modes of Schwarzschild anti-de Sitter black holes: Electromagnetic and gravitational perturbations, Phys. Rev. D 64 (2001) 084017 [gr-qc/0105103] [SPIRES].MathSciNetADSGoogle Scholar
  30. [30]
    E. Berti, V. Cardoso and P. Pani, Breit-Wigner resonances and the quasinormal modes of anti-de Sitter black holes, Phys. Rev. D 79 (2009) 101501 [arXiv:0903.5311] [SPIRES].MathSciNetADSGoogle Scholar
  31. [31]
    V. Cardoso and J.P.S. Lemos, Quasi-normal modes of toroidal, cylindrical and planar black holes in anti-de Sitter spacetimes, Class. Quant. Grav. 18 (2001) 5257 [gr-qc/0107098] [SPIRES].MathSciNetADSMATHCrossRefGoogle Scholar
  32. [32]
    R. Baier, P. Romatschke, D.T. Son, A.O. Starinets and M.A. Stephanov, Relativistic viscous hydrodynamics, conformal invariance and holography, JHEP 04 (2008) 100 [arXiv:0712.2451] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  33. [33]
    M. Natsuume, String theory implications on causal hydrodynamics, Prog. Theor. Phys. Suppl. 174 (2008) 286 [arXiv:0807.1394] [SPIRES].ADSCrossRefGoogle Scholar
  34. [34]
    M. Natsuume and T. Okamura, Causal hydrodynamics of gauge theory plasmas from AdS/CFT duality, Phys. Rev. D 77 (2008) 066014 [arXiv:0712.2916] [SPIRES].MathSciNetADSGoogle Scholar
  35. [35]
    G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics, JHEP 09 (2002) 043 [hep-th/0205052] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  36. [36]
    G.D. Moore and K.A. Sohrabi, Kubo Formulae for Second-Order Hydrodynamic Coefficients, Phys. Rev. Lett. 106 (2011) 122302 [arXiv:1007.5333] [SPIRES].ADSCrossRefGoogle Scholar
  37. [37]
    N. Banerjee and S. Dutta, Shear Viscosity to Entropy Density Ratio in Six Derivative Gravity, JHEP 07 (2009) 024 [arXiv:0903.3925] [SPIRES].ADSCrossRefGoogle Scholar
  38. [38]
    A. Buchel, R.C. Myers and A. Sinha, Beyond η s =1/4π, JHEP 03 (2009) 084 [arXiv:0812.2521] [SPIRES].ADSCrossRefGoogle Scholar
  39. [39]
    N. Banerjee and S. Dutta, Higher Derivative Corrections to Shear Viscosity from Graviton’s Effective Coupling, JHEP 03 (2009) 116 [arXiv:0901.3848] [SPIRES].ADSCrossRefGoogle Scholar
  40. [40]
    M. Brigante, H. Liu, R.C. Myers, S. Shenker and S. Yaida, Viscosity Bound Violation in Higher Derivative Gravity, Phys. Rev. D 77 (2008) 126006 [arXiv:0712.0805] [SPIRES].ADSGoogle Scholar
  41. [41]
    S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a Holographic Superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [SPIRES].ADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  1. 1.CENTRA, Departamento de Física, Instituto Superior TécnicoUniversidade Técnica de Lisboa — UTLLisboaPortugal
  2. 2.Department of Physics and AstronomyThe University of MississippiUniversityU.S.A.

Personalised recommendations