Static BPS black holes in AdS4 with general dyonic charges

  • Nick HalmagyiEmail author
Open Access
Regular Article - Theoretical Physics


We complete the study of static BPS, asymptotically AdS4 black holes within \( \mathcal{N} \) =2 FI-gauged supergravity and where the scalar manifold is a symmetric very special Kähler manifold. We find the analytic form for the general solution to the BPS equations, the horizon appears as a double root of a particular quartic polynomial whereas in previous work this quartic polynomial further factored into a pair of double roots. A new and distinguishing feature of our solutions is that the phase of the supersymmetry parameter varies throughout the black hole. The general solution has 2n v independent parameters; there are two algebraic constraints on 2n v + 2 charges, matching our previous analysis on BPS solutions of the form AdS2 × Σ g . As a consequence we have proved that every BPS geometry of this form can arise as the horizon geometry of a BPS AdS4 black hole. When specialized to the STU-model our solutions uplift to M-theory and describe a stack of M2-branes wrapped on a Riemman surface in a Calabi-Yau fivefold with internal angular momentum.


Gauge-gravity correspondence Black Holes in String Theory AdS-CFT Correspondence Supergravity Models 


Open Access

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  1. [1]
    A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  2. [2]
    J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].CrossRefzbMATHMathSciNetGoogle Scholar
  3. [3]
    S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  4. [4]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].ADSzbMATHMathSciNetGoogle Scholar
  5. [5]
    K. Behrndt, D. Lüst and W.A. Sabra, Stationary solutions of N = 2 supergravity, Nucl. Phys. B 510 (1998) 264 [hep-th/9705169] [INSPIRE].CrossRefADSGoogle Scholar
  6. [6]
    B. Bates and F. Denef, Exact solutions for supersymmetric stationary black hole composites, JHEP 11 (2011) 127 [hep-th/0304094] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  7. [7]
    S.L. Cacciatori and D. Klemm, Supersymmetric AdS 4 black holes and attractors, JHEP 01 (2010) 085 [arXiv:0911.4926] [INSPIRE].CrossRefADSMathSciNetGoogle 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] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  9. [9]
    K. Hristov and S. Vandoren, Static supersymmetric black holes in AdS 4 with spherical symmetry, JHEP 04 (2011) 047 [arXiv:1012.4314] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  10. [10]
    N. Halmagyi, BPS Black Hole Horizons in N = 2 Gauged Supergravity, JHEP 02 (2014) 051 [arXiv:1308.1439] [INSPIRE].CrossRefADSGoogle Scholar
  11. [11]
    N. Halmagyi and T. Vanel, AdS Black Holes from Duality in Gauged Supergravity, JHEP 04 (2014) 130 [arXiv:1312.5430] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  12. [12]
    S. Katmadas, Static BPS black holes in U(1) gauged supergravity, JHEP 09 (2014) 027 [arXiv:1405.4901] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  13. [13]
    J.M. Maldacena and C. Núñez, Supergravity description of field theories on curved manifolds and a no go theorem, Int. J. Mod. Phys. A 16 (2001) 822 [hep-th/0007018] [INSPIRE].CrossRefADSGoogle Scholar
  14. [14]
    J.P. Gauntlett, N. Kim, S. Pakis and D. Waldram, Membranes wrapped on holomorphic curves, Phys. Rev. D 65 (2002) 026003 [hep-th/0105250] [INSPIRE].ADSMathSciNetGoogle Scholar
  15. [15]
    M.M. Caldarelli and D. Klemm, Supersymmetry of Anti-de Sitter black holes, Nucl. Phys. B 545 (1999) 434 [hep-th/9808097] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  16. [16]
    F. Denef, Supergravity flows and D-brane stability, JHEP 08 (2000) 050 [hep-th/0005049] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  17. [17]
    A. Gnecchi and N. Halmagyi, Supersymmetric black holes in AdS 4 from very special geometry, JHEP 04 (2014) 173 [arXiv:1312.2766] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  18. [18]
    N. Halmagyi, M. Petrini and A. Zaffaroni, BPS black holes in AdS 4 from M-theory, JHEP 08 (2013) 124 [arXiv:1305.0730] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  19. [19]
    M. Cvetič et al., Embedding AdS black holes in ten-dimensions and eleven-dimensions, Nucl. Phys. B 558 (1999) 96 [hep-th/9903214] [INSPIRE].CrossRefADSGoogle Scholar
  20. [20]
    B. de Wit and H. Nicolai, N = 8 Supergravity, Nucl. Phys. B 208 (1982) 323 [INSPIRE].CrossRefADSGoogle Scholar
  21. [21]
    B. de Wit and H. Nicolai, The Consistency of the S 7 Truncation in D = 11 Supergravity, Nucl. Phys. B 281 (1987) 211 [INSPIRE].CrossRefADSGoogle Scholar
  22. [22]
    H. Nicolai and K. Pilch, Consistent Truncation of D = 11 Supergravity on AdS 4 × S 7, JHEP 03 (2012) 099 [arXiv:1112.6131] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  23. [23]
    D.D.K. Chow and G. Compère, Dyonic AdS black holes in maximal gauged supergravity, Phys. Rev. D 89 (2014) 065003 [arXiv:1311.1204] [INSPIRE].ADSGoogle Scholar
  24. [24]
    D. Klemm and O. Vaughan, Nonextremal black holes in gauged supergravity and the real formulation of special geometry, JHEP 01 (2013) 053 [arXiv:1207.2679] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  25. [25]
    D. Klemm and O. Vaughan, Nonextremal black holes in gauged supergravity and the real formulation of special geometry II, Class. Quant. Grav. 30 (2013) 065003 [arXiv:1211.1618] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  26. [26]
    A. Gnecchi and C. Toldo, On the non-BPS first order flow in N = 2 U(1)-gauged Supergravity, JHEP 03 (2013) 088 [arXiv:1211.1966] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  27. [27]
    K. Hristov, C. Toldo and S. Vandoren, Phase transitions of magnetic AdS 4 black holes with scalar hair, Phys. Rev. D 88 (2013) 026019 [arXiv:1304.5187] [INSPIRE].ADSGoogle Scholar
  28. [28]
    A. Gnecchi and C. Toldo, First order flow for non-extremal AdS black holes and mass from holographic renormalization, JHEP 10 (2014) 075 [arXiv:1406.0666] [INSPIRE].CrossRefADSGoogle Scholar
  29. [29]
    S. Barisch, G. Lopes Cardoso, M. Haack, S. Nampuri and N.A. Obers, Nernst branes in gauged supergravity, JHEP 11 (2011) 090 [arXiv:1108.0296] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  30. [30]
    K. Goldstein, S. Nampuri and Á. Véliz-Osorio, Heating up branes in gauged supergravity, JHEP 08 (2014) 151 [arXiv:1406.2937] [INSPIRE].CrossRefADSGoogle Scholar
  31. [31]
    H. Lü, Y. Pang and C.N. Pope, AdS Dyonic Black Hole and its Thermodynamics, JHEP 11 (2013) 033 [arXiv:1307.6243] [INSPIRE].CrossRefGoogle Scholar
  32. [32]
    J.F. Plebanski and M. Demianski, Rotating, charged and uniformly accelerating mass in general relativity, Annals Phys. 98 (1976) 98 [INSPIRE].CrossRefADSzbMATHMathSciNetGoogle Scholar
  33. [33]
    D. Klemm and M. Nozawa, Supersymmetry of the C-metric and the general Plebanski-Demianski solution, JHEP 05 (2013) 123 [arXiv:1303.3119] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  34. [34]
    V.A. Kostelecky and M.J. Perry, Solitonic black holes in gauged N = 2 supergravity, Phys. Lett. B 371 (1996) 191 [hep-th/9512222] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  35. [35]
    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] [INSPIRE].CrossRefADSGoogle Scholar
  36. [36]
    D. Klemm, Rotating BPS black holes in matter-coupled AdS 4 supergravity, JHEP 07 (2011) 019 [arXiv:1103.4699] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  37. [37]
    A. Gnecchi, K. Hristov, D. Klemm, C. Toldo and O. Vaughan, Rotating black holes in 4d gauged supergravity, JHEP 01 (2014) 127 [arXiv:1311.1795] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  38. [38]
    A. Donos and J.P. Gauntlett, Supersymmetric quantum criticality supported by baryonic charges, JHEP 10 (2012) 120 [arXiv:1208.1494] [INSPIRE].CrossRefADSGoogle Scholar
  39. [39]
    D. Cassani, P. Koerber and O. Varela, All homogeneous N = 2 M-theory truncations with supersymmetric AdS4 vacua, JHEP 11 (2012) 173 [arXiv:1208.1262] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  40. [40]
    N. Bobev, N. Halmagyi, K. Pilch and N.P. Warner, Supergravity Instabilities of Non-Supersymmetric Quantum Critical Points, Class. Quant. Grav. 27 (2010) 235013 [arXiv:1006.2546] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  41. [41]
    B. de Wit and A. Van Proeyen, Special geometry, cubic polynomials and homogeneous quaternionic spaces, Commun. Math. Phys. 149 (1992) 307 [hep-th/9112027] [INSPIRE].CrossRefADSzbMATHGoogle Scholar
  42. [42]
    B. de Wit, F. Vanderseypen and A. Van Proeyen, Symmetry structure of special geometries, Nucl. Phys. B 400 (1993) 463 [hep-th/9210068] [INSPIRE].CrossRefADSGoogle Scholar
  43. [43]
    B. de Wit and A. Van Proeyen, Hidden symmetries, special geometry and quaternionic manifolds, Int. J. Mod. Phys. D 3 (1994) 31 [hep-th/9310067] [INSPIRE].CrossRefADSGoogle Scholar
  44. [44]
    B. de Wit and A. Van Proeyen, Isometries of special manifolds, hep-th/9505097 [INSPIRE].
  45. [45]
    M. Cvetič and A.A. Tseytlin, Solitonic strings and BPS saturated dyonic black holes, Phys. Rev. D 53 (1996) 5619 [Erratum ibid. D 55 (1997) 3907] [hep-th/9512031] [INSPIRE].
  46. [46]
    R. Kallosh and B. Kol, E 7 symmetric area of the black hole horizon, Phys. Rev. D 53 (1996) 5344 [hep-th/9602014] [INSPIRE].ADSMathSciNetGoogle Scholar
  47. [47]
    M. Cvetič and C.M. Hull, Black holes and U duality, Nucl. Phys. B 480 (1996) 296 [hep-th/9606193] [INSPIRE].CrossRefADSGoogle Scholar
  48. [48]
    B.L. Cerchiai, S. Ferrara, A. Marrani and B. Zumino, Duality, Entropy and ADM Mass in Supergravity, Phys. Rev. D 79 (2009) 125010 [arXiv:0902.3973] [INSPIRE].ADSMathSciNetGoogle Scholar
  49. [49]
    S. Ferrara, A. Marrani and A. Yeranyan, On Invariant Structures of Black Hole Charges, JHEP 02 (2012) 071 [arXiv:1110.4004] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  50. [50]
    G. Bossard and S. Katmadas, Duality covariant non-BPS first order systems, JHEP 09 (2012) 100 [arXiv:1205.5461] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.Sorbonne Universités, UPMC Paris 06, UMR 7589, LPTHEParisFrance
  2. 2.CNRS, UMR 7589, LPTHEParisFrance

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