Hidden conformal symmetry for vector field on various black hole backgrounds

Open Access
Regular Article - Theoretical Physics

Abstract

Hidden conformal symmetries of scalar field on various black hole backgrounds have been investigated for years, but whether those features hold for other fields are still open questions. Recently, with proper assumptions, Lunin achieved to the separation of variables for Maxwell equations on Kerr background. In this paper, with that equation, we find that hidden conformal symmetry appears at near region under low frequency limit. We also extended those results to vector field on the more general Kerr-NUT-(A)dS background, then hidden conformal symmetry also appears if we focusing on the near-horizon region at low frequency limit.

Keywords

Black Holes Conformal and W Symmetry AdS-CFT Correspondence Space-Time Symmetries 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    G. ’t Hooft, Dimensional reduction in quantum gravity, Conf. Proc. C 930308 (1993) 284 [gr-qc/9310026] [INSPIRE].
  2. [2]
    L. Susskind, The World as a hologram, J. Math. Phys. 36 (1995) 6377 [hep-th/9409089] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    A. Strominger, Black hole entropy from near horizon microstates, JHEP 02 (1998) 009 [hep-th/9712251] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    G. Compère, The Kerr/CFT correspondence and its extensions, Living Rev. Rel. 15 (2012) 11 [arXiv:1203.3561] [INSPIRE].CrossRefMATHGoogle Scholar
  8. [8]
    M. Guica, T. Hartman, W. Song and A. Strominger, The Kerr/CFT Correspondence, Phys. Rev. D 80 (2009) 124008 [arXiv:0809.4266] [INSPIRE].ADSMathSciNetGoogle Scholar
  9. [9]
    A. Castro and F. Larsen, Near Extremal Kerr Entropy from AdS 2 Quantum Gravity, JHEP 12 (2009) 037 [arXiv:0908.1121] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    I. Bredberg, T. Hartman, W. Song and A. Strominger, Black Hole Superradiance From Kerr/CFT, JHEP 04 (2010) 019 [arXiv:0907.3477] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    H. Lü, J. Mei and C.N. Pope, Kerr/CFT Correspondence in Diverse Dimensions, JHEP 04 (2009) 054 [arXiv:0811.2225] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  12. [12]
    Y. Matsuo, T. Tsukioka and C.-M. Yoo, Another Realization of Kerr/CFT Correspondence, Nucl. Phys. B 825 (2010) 231 [arXiv:0907.0303] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  13. [13]
    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] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  14. [14]
    M. Cvetič and F. Larsen, Greybody Factors and Charges in Kerr/CFT, JHEP 09 (2009) 088 [arXiv:0908.1136] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  15. [15]
    B. Chen and C.-S. Chu, Real-Time Correlators in Kerr/CFT Correspondence, JHEP 05 (2010) 004 [arXiv:1001.3208] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  16. [16]
    S. Carlip, Extremal and nonextremal Kerr/CFT correspondences, JHEP 04 (2011) 076 [Erratum ibid. 01 (2012) 008] [arXiv:1101.5136] [INSPIRE].
  17. [17]
    H. Lü, J.-w. Mei, C.N. Pope and J.F. Vazquez-Poritz, Extremal Static AdS Black Hole/CFT Correspondence in Gauged Supergravities, Phys. Lett. B 673 (2009) 77 [arXiv:0901.1677] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  18. [18]
    J. Mei, The Entropy for General Extremal Black Holes, JHEP 04 (2010) 005 [arXiv:1002.1349] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  19. [19]
    J. Mei, On the General Kerr/CFT Correspondence in Arbitrary Dimensions, JHEP 04 (2012) 113 [arXiv:1202.4156] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  20. [20]
    T. Azeyanagi, N. Ogawa and S. Terashima, Holographic Duals of Kaluza-Klein Black Holes, JHEP 04 (2009) 061 [arXiv:0811.4177] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  21. [21]
    T. Hartman, K. Murata, T. Nishioka and A. Strominger, CFT Duals for Extreme Black Holes, JHEP 04 (2009) 019 [arXiv:0811.4393] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  22. [22]
    D.D.K. Chow, M. Cvetič, H. Lü and C.N. Pope, Extremal Black Hole/CFT Correspondence in (Gauged) Supergravities, Phys. Rev. D 79 (2009) 084018 [arXiv:0812.2918] [INSPIRE].ADSMathSciNetGoogle Scholar
  23. [23]
    C. Shi and J. Mei, Extended Symmetries at Black Hole Horizons in Generic Dimensions, Phys. Rev. D 95 (2017) 104053 [arXiv:1611.09491] [INSPIRE].ADSGoogle Scholar
  24. [24]
    J.-J. Peng and S.-Q. Wu, Extremal Kerr black hole/CFT correspondence in the five dimensional Godel universe, Phys. Lett. B 673 (2009) 216 [arXiv:0901.0311] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    G. Compere, K. Murata and T. Nishioka, Central Charges in Extreme Black Hole/CFT Correspondence, JHEP 05 (2009) 077 [arXiv:0902.1001] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  26. [26]
    A. Castro, A. Maloney and A. Strominger, Hidden Conformal Symmetry of the Kerr Black Hole, Phys. Rev. D 82 (2010) 024008 [arXiv:1004.0996] [INSPIRE].ADSMathSciNetGoogle Scholar
  27. [27]
    B. Chen and J. Long, Hidden Conformal Symmetry and Quasi-normal Modes, Phys. Rev. D 82 (2010) 126013 [arXiv:1009.1010] [INSPIRE].ADSGoogle Scholar
  28. [28]
    B. Chen, J.-j. Zhang and J.-d. Zhang, Quasi-normal Modes and Hidden Conformal Symmetry of Warped dS 3 Black Hole, Phys. Rev. D 84 (2011) 124039 [arXiv:1110.3991] [INSPIRE].ADSGoogle Scholar
  29. [29]
    C.-M. Chen and J.-R. Sun, Hidden Conformal Symmetry of the Reissner-Nordstrøm Black Holes, JHEP 08 (2010) 034 [arXiv:1004.3963] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  30. [30]
    Y.-Q. Wang and Y.-X. Liu, Hidden Conformal Symmetry of the Kerr-Newman Black Hole, JHEP 08 (2010) 087 [arXiv:1004.4661] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  31. [31]
    B. Chen and J.-j. Zhang, General Hidden Conformal Symmetry of 4D Kerr-Newman and 5D Kerr Black Holes, JHEP 08 (2011) 114 [arXiv:1107.0543] [INSPIRE].ADSMathSciNetMATHGoogle Scholar
  32. [32]
    B. Chen, C.-M. Chen and B. Ning, Holographic Q-picture of Kerr-Newman-AdS-dS Black Hole, Nucl. Phys. B 853 (2011) 196 [arXiv:1010.1379] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  33. [33]
    B. Chen and J. Long, On Holographic description of the Kerr-Newman-AdS-dS black holes, JHEP 08 (2010) 065 [arXiv:1006.0157] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  34. [34]
    B. Chen, J. Long and J.-j. Zhang, Hidden Conformal Symmetry of Extremal Black Holes, Phys. Rev. D 82 (2010) 104017 [arXiv:1007.4269] [INSPIRE].ADSGoogle Scholar
  35. [35]
    B. Chen, A.M. Ghezelbash, V. Kamali and M.R. Setare, Holographic description of Kerr-Bolt-AdS-dS Spacetimes, Nucl. Phys. B 848 (2011) 108 [arXiv:1009.1497] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  36. [36]
    D. Bak, B. Chen and J.-B. Wu, Holographic Correlation Functions for Open Strings and Branes, JHEP 06 (2011) 014 [arXiv:1103.2024] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  37. [37]
    D.A. Lowe, I. Messamah and A. Skanata, Hidden Kerr/CFT correspondence at finite frequencies, Phys. Rev. D 89 (2014) 064005 [arXiv:1309.6574] [INSPIRE].ADSGoogle Scholar
  38. [38]
    O. Lunin, Maxwell’s equations in the Myers-Perry geometry, JHEP 12 (2017) 138 [arXiv:1708.06766] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  39. [39]
    W. Chen, H. Lü and C.N. Pope, General Kerr-NUT-AdS metrics in all dimensions, Class. Quant. Grav. 23 (2006) 5323 [hep-th/0604125] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  40. [40]
    B. Carter, Hamilton-Jacobi and Schrödinger separable solutions of Einstein’s equations, Commun. Math. Phys. 10 (1968) 280 [INSPIRE].ADSCrossRefMATHGoogle Scholar
  41. [41]
    V.P. Frolov, P. Krtouš and D. Kubizňák, Separation of variables in Maxwell equations in Plebanski-Demianski spacetime, arXiv:1802.09491 [INSPIRE].

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.TianQin Research Center for Gravitational PhysicsSun Yat-sen University (Zhuhai Campus)ZhuhaiChina
  2. 2.School of Physics and AstronomySun Yat-sen University (Zhuhai Campus)ZhuhaiChina
  3. 3.MOE Key Laboratory of Fundamental Physical Quantities Measurement, School of PhysicsHuazhong University of Science and TechnologyWuhanChina

Personalised recommendations