Journal of High Energy Physics

, 2010:62 | Cite as

Extremal limits of the Cvetič-Youm black hole and nilpotent orbits of G2(2)

Article
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Abstract

We study extremal cohomogeneity one five-dimensional asymptotically flat black holes of minimal supergravity in terms of the geodesics generated by nilpotent elements of the Lie algebra \( {\mathfrak{g}} \) 2(2) on the coset manifold G2(2) /SO(2, 2). There are two branches of regular extremal black holes with these properties: (i) the supersymmetric BMPV branch, and (ii) the non-supersymmetric extremal branch. We show that both of these branches are reproduced by nilpotent SO(2, 2)-orbits. Furthermore, we show that the partial ordering of nilpotent orbits of G2(2) is in one-to-one correspondence with the phase diagram of these extremal black holes.

Keywords

Black Holes in String Theory Space-Time Symmetries 
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References

  1. [1]
    A. Ceresole and G. Dall’Agata, Flow equations for non-BPS extremal black holes, JHEP 03 (2007) 110 [hep-th/0702088] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  2. [2]
    L. Andrianopoli, R. D’Auria, E. Orazi and M. Trigiante, First order description of black holes in moduli space, JHEP 11 (2007) 032 [arXiv:0706.0712] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  3. [3]
    K. Hotta and T. Kubota, Exact solutions and the attractor mechanism in non-BPS black holes, Prog. Theor. Phys. 118 (2007) 969 [arXiv:0707.4554] [SPIRES].MATHCrossRefADSGoogle Scholar
  4. [4]
    D. Gaiotto, W. Li and M. Padi, Non-supersymmetric attractor flow in symmetric spaces, JHEP 12 (2007) 093 [arXiv:0710.1638] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  5. [5]
    E.G. Gimon, F. Larsen and J. Simon, Black holes in supergravity: the non-BPS branch, JHEP 01 (2008) 040 [arXiv:0710.4967] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  6. [6]
    E. Bergshoeff, W. Chemissany, A. Ploegh, M. Trigiante and T. Van Riet, Generating geodesic flows and supergravity solutions, Nucl. Phys. B 812 (2009) 343 [arXiv:0806.2310] [SPIRES]. CrossRefADSGoogle Scholar
  7. [7]
    S. Bellucci, S. Ferrara, A. Marrani and A. Yeranyan, STU black holes unveiled, arXiv:0807.3503 [SPIRES].
  8. [8]
    J. Perz, P. Smyth, T. Van Riet and B. Vercnocke, First-order flow equations for extremal and non-extremal black holes, JHEP 03 (2009) 150 [arXiv:0810.1528] [SPIRES].CrossRefADSGoogle Scholar
  9. [9]
    G. Bossard, H. Nicolai and K.S. Stelle, Universal BPS structure of stationary supergravity solutions, JHEP 07 (2009) 003 [arXiv:0902.4438] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  10. [10]
    G. Compere, S. de Buyl, E. Jamsin and A. Virmani, G 2 dualities in D =5 supergravity and black strings, Class. Quant. Grav. 26 (2009) 125016 [arXiv:0903.1645] [SPIRES].CrossRefADSGoogle Scholar
  11. [11]
    W. Chemissany, J. Rosseel, M. Trigiante and T. Van Riet, The full integration of black hole solutions to symmetric supergravity theories, Nucl. Phys. B 830 (2010) 391 [arXiv:0903.2777] [SPIRES].CrossRefADSGoogle Scholar
  12. [12]
    S. Bellucci, S. Ferrara, M. Günaydin and A. Marrani, SAM lectures on extremal black holes in D =4 extended supergravity, arXiv:0905.3739 [SPIRES].
  13. [13]
    G. Bossard, The extremal black holes of N =4 supergravity from so(8,2+n) nilpotent orbits, Gen. Rel. Grav. 42 (2010) 539 [arXiv:0906.1988] [SPIRES].MATHCrossRefMathSciNetADSGoogle Scholar
  14. [14]
    M. Günaydin, Lectures on spectrum generating symmetries and U-duality in supergravity, extremal black holes, quantum attractors and harmonic superspace, arXiv:0908.0374 [SPIRES].
  15. [15]
    G. Bossard, Y. Michel and B. Pioline, Extremal black holes, nilpotent orbits and the true fake superpotential, JHEP 01 (2010) 038 [arXiv:0908.1742] [SPIRES].CrossRefADSGoogle Scholar
  16. [16]
    S. Ferrara, A. Marrani and E. Orazi, Maurer-Cartan equations and black hole superpotentials in N =8 supergravity, Phys. Rev. D 81 (2010) 085013 [arXiv:0911.0135] [SPIRES].ADSGoogle Scholar
  17. [17]
    S.-S. Kim, J.L. Hornlund, J. Palmkvist and A. Virmani, Extremal solutions of the S 3 model and nilpotent orbits of G 2(2), JHEP 08 (2010) 072 [arXiv:1004.5242] [SPIRES].CrossRefADSGoogle Scholar
  18. [18]
    P. Meessen, T. Ortín, S. Vaula, T. Ortín and S. Vaula, All the timelike supersymmetric solutions of all ungauged D =4 supergravities, arXiv:1006.0239 [SPIRES].
  19. [19]
    W. Chemissany et al., Black holes in supergravity and integrability, JHEP 09 (2010) 080 [arXiv:1007.3209] [SPIRES].CrossRefADSGoogle Scholar
  20. [20]
    G. Compere, S. de Buyl, S. Stotyn and A. Virmani, A general black string and its microscopics, arXiv:1006.5464 [SPIRES].
  21. [21]
    S. Giusto and A. Saxena, Stationary axisymmetric solutions of five dimensional gravity, Class. Quant. Grav. 24 (2007) 4269 [arXiv:0705.4484] [SPIRES].MATHCrossRefMathSciNetADSGoogle Scholar
  22. [22]
    A. Bouchareb et al., G 2 generating technique for minimal D =5 supergravity and black rings, Phys. Rev. D 76 (2007) 104032 [arXiv:0708.2361] [SPIRES].MathSciNetADSGoogle Scholar
  23. [23]
    J. Ford, S. Giusto, A. Peet and A. Saxena, Reduction without reduction: adding KK-monopoles to five dimensional stationary axisymmetric solutions, Class. Quant. Grav. 25 (2008) 075014 [arXiv:0708.3823] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  24. [24]
    S. Giusto, S.F. Ross and A. Saxena, Non-supersymmetric microstates of the D1-D5-KK system, JHEP 12 (2007) 065 [arXiv:0708.3845] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  25. [25]
    D.V. Gal’tsov and N.G. Scherbluk, Generating technique for U(1)3 5D supergravity, Phys. Rev. D 78 (2008) 064033 [arXiv:0805.3924] [SPIRES].MathSciNetADSGoogle Scholar
  26. [26]
    J. Camps, R. Emparan, P. Figueras, S. Giusto and A. Saxena, Black rings in Taub-NUT and D0-D6 interactions, JHEP 02 (2009) 021 [arXiv:0811.2088] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  27. [27]
    D.V. Gal’tsov and N.G. Scherbluk, Three-charge doubly rotating black ring, Phys. Rev. D 81 (2010) 044028 [arXiv:0912.2771] [SPIRES].ADSGoogle Scholar
  28. [28]
    M. Berkooz and B. Pioline, 5D black holes and non-linear σ-models, JHEP 05 (2008) 045 [arXiv:0802.1659] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  29. [29]
    H. Elvang, R. Emparan and P. Figueras, Non-supersymmetric black rings as thermally excited supertubes, JHEP 02 (2005) 031 [hep-th/0412130] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  30. [30]
    M. Cvetič and F. Larsen, General rotating black holes in string theory: greybody factors and event horizons, Phys. Rev. D 56 (1997) 4994 [hep-th/9705192] [SPIRES].ADSGoogle Scholar
  31. [31]
    M. Cvetič and D. Youm, General rotating five dimensional black holes of toroidally compactified heterotic string, Nucl. Phys. B 476 (1996) 118 [hep-th/9603100] [SPIRES].CrossRefADSGoogle Scholar
  32. [32]
    S. Giusto, S.D. Mathur and A. Saxena, Dual geometries for a set of 3-charge microstates, Nucl. Phys. B 701 (2004) 357 [hep-th/0405017] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  33. [33]
    V. Jejjala, O. Madden, S.F. Ross and G. Titchener, Non-supersymmetric smooth geometries and D1-D5-P bound states, Phys. Rev. D 71 (2005) 124030 [hep-th/0504181] [SPIRES].MathSciNetADSGoogle Scholar
  34. [34]
    O.J.C. Dias, R. Emparan and A. Maccarrone, Microscopic theory of black hole superradiance, Phys. Rev. D 77 (2008) 064018 [arXiv:0712.0791] [SPIRES].MathSciNetADSGoogle Scholar
  35. [35]
    J.C. Breckenridge, R.C. Myers, A.W. Peet and C. Vafa, D-branes and spinning black holes, Phys. Lett. B 391 (1997) 93 [hep-th/9602065] [SPIRES].MathSciNetADSGoogle Scholar
  36. [36]
    G.W. Gibbons and C.A.R. Herdeiro, Supersymmetric rotating black holes and causality violation, Class. Quant. Grav. 16 (1999) 3619 [hep-th/9906098] [SPIRES].MATHCrossRefMathSciNetADSGoogle Scholar
  37. [37]
    P. Breitenlohner, D. Maison and G.W. Gibbons, Four-dimensional black holes from Kaluza-Klein theories, Commun. Math. Phys. 120 (1988) 295 [SPIRES].MATHCrossRefMathSciNetADSGoogle Scholar
  38. [38]
    D. Collingwood and W. McGovern, Nilpotent orbits in semisimple Lie algebras, Springer, U.S.A. (1993).Google Scholar
  39. [39]
    D. Djokovic, The closure diagrams for nilpotent orbits of real forms of f 4 and g 2, J. Lie Theory 10 (2000) 491MATHMathSciNetGoogle Scholar
  40. [40]
    P. Figueras, E. Jamsin, J.V. Rocha and A. Virmani, Integrability of five dimensional minimalsupergravity and charged rotating black holes, Class. Quant. Grav. 27 (2010) 135011 [arXiv:0912.3199] [SPIRES].CrossRefADSGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  1. 1.Physique Théorique et MathématiqueUniversité Libre de Bruxelles and International Solvay InstitutesBruxellesBelgium

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