Scattering of gravitational and electromagnetic waves off AdS2 × S2 in extreme Reissner-Nordstrom

  • Achilleas P. PorfyriadisEmail author
Open Access
Regular Article - Theoretical Physics


The direct product of two-dimensional anti-de Sitter spacetime with a two-sphere is an exact solution of four-dimensional Einstein-Maxwell theory without a cosmological constant. In this paper, we analytically solve the coupled gravitational and electromagnetic perturbation equations of AdS2 × S2 in Einstein-Maxwell theory. On the other hand, AdS2 × S2 also describes the near-horizon region of the extreme Reissner-Nordstrom (ERN) black hole. We therefore also solve the connection problem: we show how the AdS2 × S2 perturbation equations arise from an appropriate near-horizon approximation of the corresponding equations for the ERN and then, using matched asymptotic expansions, we analytically extend the AdS2 × S2 solutions away from the near-horizon region connecting them with solutions in the far asymptotically flat region. From the point of view of ERN our results may be thought of as computing the classical scattering matrix for gravitational and electromagnetic waves which probe the near-horizon region of the black hole.


2D Gravity AdS-CFT Correspondence Black Holes 


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.


  1. [1]
    G. Sárosi, AdS 2 holography and the SYK model, PoS(Modave2017)001 [arXiv:1711.08482] [INSPIRE].
  2. [2]
    J. Maldacena and X.-L. Qi, Eternal traversable wormhole, arXiv:1804.00491 [INSPIRE].
  3. [3]
    D. Harlow and D. Jafferis, The Factorization Problem in Jackiw-Teitelboim Gravity, arXiv:1804.01081 [INSPIRE].
  4. [4]
    B. Bertotti, Uniform electromagnetic field in the theory of general relativity, Phys. Rev. 116 (1959) 1331 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    I. Robinson, A Solution of the Maxwell-Einstein Equations, Bull. Acad. Pol. Sci. Ser. Sci. Math. Astron. Phys. 7 (1959) 351 [INSPIRE].MathSciNetzbMATHGoogle Scholar
  6. [6]
    J.M. Maldacena, J. Michelson and A. Strominger, Anti-de Sitter fragmentation, JHEP 02 (1999) 011 [hep-th/9812073] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    S. Chandrasekhar, The mathematical theory of black holes, Clarendon Press, Oxford, England, (1985).Google Scholar
  8. [8]
    A. Ishibashi and H. Kodama, Perturbations and Stability of Static Black Holes in Higher Dimensions, Prog. Theor. Phys. Suppl. 189 (2011) 165 [arXiv:1103.6148] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  9. [9]
    A.A. Starobinsky, Amplification of waves reflected from a rotating “black hole”, Sov. Phys. JETP 37 (1973) 28 [Zh. Eksp. Teor. Fiz. 64 (1973) 48] [INSPIRE].
  10. [10]
    A.A. Starobinskil and S.M. Churilov, Amplification of electromagnetic and gravitational waves scattered by a rotating “black hole”, Sov. Phys. JETP 65 (1974) 1 [INSPIRE].ADSGoogle Scholar
  11. [11]
    S.A. Teukolsky and W.H. Press, Perturbations of a rotating black hole. III — Interaction of the hole with gravitational and electromagnet ic radiation, Astrophys. J. 193 (1974) 443 [INSPIRE].
  12. [12]
    A.P. Porfyriadis, Y. Shi and A. Strominger, Photon Emission Near Extreme Kerr Black Holes, Phys. Rev. D 95 (2017) 064009 [arXiv:1607.06028] [INSPIRE].
  13. [13]
    R. Fabbri, Electromagnetic and Gravitational Waves in the Background of a Reissner-Nordstrom Black Hole, Nuovo Cim. B 40 (1977) 311 [INSPIRE].
  14. [14]
    L.C.B. Crispino, A. Higuchi and G.E.A. Matsas, Low-frequency absorption cross section of the electromagnetic waves for the extreme Reissner-Nordstrom black holes in higher dimensions, Phys. Rev. D 82 (2010) 124038 [arXiv:1004.4018] [INSPIRE].
  15. [15]
    A.P. Porfyriadis, Near-AdS 2 perturbations and the connection with near-extreme Reissner-Nordstrom, arXiv:1806.07097 [INSPIRE].
  16. [16]
    T. Regge and J.A. Wheeler, Stability of a Schwarzschild singularity, Phys. Rev. 108 (1957) 1063 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    F.J. Zerilli, Perturbation analysis for gravitational and electromagnetic radiation in a Reissner-Nordström geometry, Phys. Rev. D 9 (1974) 860 [INSPIRE].
  18. [18]
    P.L. Chrzanowski and C.W. Misner, Geodesic synchrotron radiation in the Kerr geometry by the method of asymptotically factorized Green’s functions, Phys. Rev. D 10 (1974) 1701 [INSPIRE].
  19. [19]
    V.P. Frolov and I.D. Novikov, Black hole physics: Basic concepts and new developments, Kluwer Academic, Dodrecht, Netherlands, (1998).Google Scholar
  20. [20]
    M. Sasaki and H. Tagoshi, Analytic black hole perturbation approach to gravitational radiation, Living Rev. Rel. 6 (2003) 6 [gr-qc/0306120] [INSPIRE].
  21. [21]
    G.J. Galloway and M. Graf, Rigidity of asymptotically AdS 2 × S 2 spacetimes, arXiv:1803.10529 [INSPIRE].
  22. [22]
    J.M. Bardeen and G.T. Horowitz, The extreme Kerr throat geometry: A vacuum analog of AdS 2 × S 2, Phys. Rev. D 60 (1999) 104030 [hep-th/9905099] [INSPIRE].
  23. [23]
    M. Guica, T. Hartman, W. Song and A. Strominger, The Kerr/CFT Correspondence, Phys. Rev. D 80 (2009) 124008 [arXiv:0809.4266] [INSPIRE].
  24. [24]
    A.J. Amsel, G.T. Horowitz, D. Marolf and M.M. Roberts, No Dynamics in the Extremal Kerr Throat, JHEP 09 (2009) 044 [arXiv:0906.2376] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  25. [25]
    O.J.C. Dias, H.S. Reall and J.E. Santos, Kerr-CFT and gravitational perturbations, JHEP 08 (2009) 101 [arXiv:0906.2380] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  26. [26]
    A.P. Porfyriadis and A. Strominger, Gravity waves from the Kerr/CFT correspondence, Phys. Rev. D 90 (2014) 044038 [arXiv:1401.3746] [INSPIRE].
  27. [27]
    S. Hadar, A.P. Porfyriadis and A. Strominger, Fast plunges into Kerr black holes, JHEP 07 (2015) 078 [arXiv:1504.07650] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    R. Jackiw, Lower Dimensional Gravity, Nucl. Phys. B 252 (1985) 343 [INSPIRE].
  29. [29]
    C. Teitelboim, Gravitation and Hamiltonian Structure in Two Space-Time Dimensions, Phys. Lett. B 126 (1983) 41 [INSPIRE].
  30. [30]
    A. Almheiri and J. Polchinski, Models of AdS 2 backreaction and holography, JHEP 11 (2015) 014 [arXiv:1402.6334] [INSPIRE].
  31. [31]
    J. Maldacena, D. Stanford and Z. Yang, Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space, PTEP 2016 (2016) 12C104 [arXiv:1606.01857] [INSPIRE].
  32. [32]
    P. Nayak, A. Shukla, R.M. Soni, S.P. Trivedi and V. Vishal, On the Dynamics of Near-Extremal Black Holes, arXiv:1802.09547 [INSPIRE].

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Department of Physics, UCSBSanta BarbaraU.S.A.

Personalised recommendations