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Rotating BPS black holes in matter-coupled AdS4 supergravity

  • Dietmar KlemmEmail author
Article

Abstract

Using the general recipe given in arXiv:0804.0009, where all timelike super-symmetric solutions of \( \mathcal{N} = 2 \), D = 4 gauged supergravity coupled to abelian vector multiplets were classified, we construct genuine rotating supersymmetric black holes in AdS4 with nonconstant scalar fields. This is done for the SU(1, 1)/U(1) model with prepotential F = −iX 0 X 1. In the static case, the black holes are uplifted to eleven dimensions, and generalize the solution found in hep-th/0105250 corresponding to membranes wrapping holomorphic curves in a Calabi-Yau five-fold. The constructed rotating black holes preserve one quarter of the supersymmetry, whereas their near-horizon geometry is one half BPS. Moreover, for constant scalars, we generalize (a supersymmetric subclass of) the Plebanski-Demianski solution of cosmological Einstein-Maxwell theory to an arbitrary number of vector multiplets. Remarkably, the latter turns out to be related to the dimensionally reduced gravitational Chern-Simons action.

Keywords

Black Holes in String Theory AdS-CFT Correspondence Superstring Vacua 

References

  1. [1]
    S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  2. [2]
    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
  3. [3]
    A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [SPIRES].MathSciNetADSGoogle Scholar
  4. [4]
    S.L. Cacciatori and D. Klemm, Supersymmetric AdS 4 black holes and attractors, JHEP 01 (2010) 085 [arXiv:0911.4926] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    S.L. Cacciatori, D. Klemm, D.S. Mansi and E. Zorzan, All timelike supersymmetric solutions of N = 2, D = 4 gauged supergravity coupled to abelian vector multiplets, JHEP 05 (2008) 097 [arXiv:0804.0009] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    L.J. Romans, Supersymmetric, cold and lukewarm black holes in cosmological Einstein-Maxwell theory, Nucl. Phys. B 383 (1992) 395 [hep-th/9203018] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  7. [7]
    K. Hristov and S. Vandoren, Static supersymmetric black holes in AdS 4 with spherical symmetry, JHEP 04 (2011) 047 [arXiv:1012.4314] [SPIRES];ADSCrossRefMathSciNetGoogle Scholar
  8. [8]
    G. Dall’Agata and A. Gnecchi, Flow equations and attractors for black holes in N = 2 U(1) gauged supergravity, JHEP 03 (2011) 037 [arXiv:1012.3756] [SPIRES].ADSCrossRefMathSciNetGoogle Scholar
  9. [9]
    V.A. Kostelecky and M.J. Perry, Solitonic black holes in gauged N = 2 supergravity, Phys. Lett. B 371 (1996) 191 [hep-th/9512222] [SPIRES].MathSciNetADSGoogle Scholar
  10. [10]
    M.M. Caldarelli and D. Klemm, Supersymmetry of anti-de Sitter black holes, Nucl. Phys. B 545 (1999) 434 [hep-th/9808097] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  11. [11]
    Z.W. Chong, M. Cvetič, H. Lü and C.N. Pope, Charged rotating black holes in four-dimensional gauged and ungauged supergravities, Nucl. Phys. B 717 (2005) 246 [hep-th/0411045] [SPIRES].ADSCrossRefGoogle Scholar
  12. [12]
    M. Cvetič, G.W. Gibbons, H. Lü and C.N. Pope, Rotating black holes in gauged supergravities: thermodynamics, supersymmetric limits, topological solitons and time machines, hep-th/0504080 [SPIRES].
  13. [13]
    S. Ferrara, R. Kallosh and A. Strominger, N = 2 extremal black holes, Phys. Rev. D 52 (1995) 5412 [hep-th/9508072] [SPIRES].MathSciNetADSGoogle Scholar
  14. [14]
    A. Strominger, Macroscopic entropy of N = 2 extremal black holes, Phys. Lett. B 383 (1996) 39 [hep-th/9602111] [SPIRES].MathSciNetADSGoogle Scholar
  15. [15]
    S. Ferrara and R. Kallosh, Supersymmetry and attractors, Phys. Rev. D 54 (1996) 1514 [hep-th/9602136] [SPIRES].MathSciNetADSGoogle Scholar
  16. [16]
    S. Ferrara and R. Kallosh, Universality of supersymmetric attractors, Phys. Rev. D 54 (1996) 1525 [hep-th/9603090] [SPIRES].MathSciNetADSGoogle Scholar
  17. [17]
    S. Ferrara, G.W. Gibbons and R. Kallosh, Black holes and critical points in moduli space, Nucl. Phys. B 500 (1997) 75 [hep-th/9702103] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  18. [18]
    J.F. Morales and H. Samtleben, Entropy function and attractors for AdS black holes, JHEP 10 (2006) 074 [hep-th/0608044] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  19. [19]
    S. Bellucci, S. Ferrara, A. Marrani and A. Yeranyan, D = 4 black hole attractors in N = 2 supergravity with Fayet-Iliopoulos terms, Phys. Rev. D 77 (2008) 085027 [arXiv:0802.0141] [SPIRES].MathSciNetADSGoogle Scholar
  20. [20]
    L. Andrianopoli et al., N = 2 supergravity and N = 2 super Yang-Mills theory on general scalar manifolds: symplectic covariance, gaugings and the momentum map, J. Geom. Phys. 23 (1997) 111 [hep-th/9605032] [SPIRES].MathSciNetADSzbMATHCrossRefGoogle Scholar
  21. [21]
    A. Van Proeyen, \( \mathcal{N} = 2 \) supergravity in d = 4, 5, 6 and its matter couplings, extended version of the lectures given at Institut Henri Poincaré, Paris France, during the semester Supergravity, superstrings and M-theory (2000) [http://itf.fys.kuleuven.ac.be/toine/home.htm#B].
  22. [22]
    S.L. Cacciatori, M.M. Caldarelli, D. Klemm and D.S. Mansi, More on BPS solutions of N = 2, D = 4 gauged supergravity, JHEP 07 (2004) 061 [hep-th/0406238] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  23. [23]
    G. Guralnik, A. Iorio, R. Jackiw and S.Y. Pi, Dimensionally reduced gravitational Chern-Simons term and its kink, Ann. Phys. 308 (2003) 222 [hep-th/0305117] [SPIRES].MathSciNetADSzbMATHCrossRefGoogle Scholar
  24. [24]
    D. Grumiller and W. Kummer, The classical solutions of the dimensionally reduced gravitational Chern-Simons theory, Ann. Phys. 308 (2003) 211 [hep-th/0306036] [SPIRES].MathSciNetADSzbMATHCrossRefGoogle Scholar
  25. [25]
    J.F. Plebanski and M. Demianski, Rotating, charged and uniformly accelerating mass in general relativity, Ann. Phys. 98 (1976) 98 [SPIRES].MathSciNetADSzbMATHCrossRefGoogle Scholar
  26. [26]
    N. Alonso-Alberca, P. Meessen and T. Ortín, Supersymmetry of topological Kerr-Newman-Taub-NUT-adS spacetimes, Class. Quant. Grav. 17 (2000) 2783 [hep-th/0003071] [SPIRES].ADSzbMATHCrossRefGoogle Scholar
  27. [27]
    D. Klemm and E. Zorzan, The timelike half-supersymmetric backgrounds of N = 2, D = 4 supergravity with Fayet-Iliopoulos gauging, Phys. Rev. D 82 (2010) 045012 [arXiv:1003.2974] [SPIRES].ADSGoogle Scholar
  28. [28]
    D. Astefanesei, K. Goldstein, R.P. Jena, A. Sen and S.P. Trivedi, Rotating attractors, JHEP 10 (2006) 058 [hep-th/0606244] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  29. [29]
    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] [SPIRES].MathSciNetADSGoogle Scholar
  30. [30]
    M. Cvetič et al., Embedding AdS black holes in ten and eleven dimensions, Nucl. Phys. B 558 (1999) 96 [hep-th/9903214] [SPIRES].ADSCrossRefGoogle Scholar
  31. [31]
    M. Cvetič, H. Lü and C.N. Pope, Four-dimensional N = 4, SO(4) gauged supergravity from D = 11, Nucl. Phys. B 574 (2000) 761 [hep-th/9910252] [SPIRES].ADSCrossRefGoogle Scholar
  32. [32]
    J.P. Gauntlett, N. Kim, S. Pakis and D. Waldram, Membranes wrapped on holomorphic curves, Phys. Rev. D 65 (2002) 026003 [hep-th/0105250] [SPIRES].MathSciNetADSGoogle Scholar
  33. [33]
    K. Hristov, H. Looyestijn and S. Vandoren, BPS black holes in N = 2 D = 4 gauged supergravities, JHEP 08 (2010) 103 [arXiv:1005.3650] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  34. [34]
    M. Colleoni and D. Klemm, Rotating supersymmetric attractors in AdS, in preparation.Google Scholar

Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  1. 1.Dipartimento di Fisica dell’Università di Milano and INFN, Sezione di MilanoMilanoItaly

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