Skip to main content

Part of the book series: Lecture Notes in Physics ((LNP,volume 737))

Abstract

We present the main features of the physics of extremal black holes embedded in supersymmetric theories of gravitation, with a detailed analysis of the attractor mechanism for BPS and non-BPS black-hole solutions in four dimensions.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 89.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 119.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. B. De Witt, C. De Witt eds.: Black Holes(Gordon and Breach, New York, 1973); S. W. Hawking, W. Israel: General Relativity(Cambridge University Press, Cambridge, 1979); R. M.Wald: General Relativity(University of Chicago Press, Chicago, 1984)

    Google Scholar 

  2. G. W. Moore: Les Houches lectures on strings and arithmetic, arXiv:hepth/0401049; M. R. Douglas, R. Reinbacher, S. T. Yau: Branes, bundles and attractors: Bogomolov and beyond, arXiv:math.ag/0604597

    Google Scholar 

  3. M. J. Du.: String triality, black-hole entropy and Cayley’s hyperdeterminant, arXiv:hep-th/0601134; R. Kallosh, A. Linde: Phys. Rev. D 73, 104033 (2006) P. Levay: Phys. Rev. D 74, 024030 (2006) M. J. Du., S. Ferrara: E7 and the tripartite entanglement of seven qubits, arXiv:quant-ph/0609227; P. Levay: Strings, black holes, the tripartite entanglement of seven qubits and the Fano plane, arXiv:hep-th/0610314

    Google Scholar 

  4. S. W. Hawking, R. Penrose: Proc. Roy. Soc. Lond. A 314, 529 (1970)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  5. G. Gibbons: in Uni.ed theories of Elementary Particles. Critical Assessment and Prospects, Proceedings of the Heisemberg Symposium, Müunchen, Germany, 1981, ed. by P. Breitenlohner, H. P. Düurr, Lecture Notes in Physics, Vol. 160 (Springer-Verlag, Berlin, 1982); G. W. Gibbons: in Supersymmetry, Supergravity and Related Topics, Proceedings of the XVth GIFT International Physics (Girona, Spain 1984), ed. by F. del Aguila, J. de Azc’arraga, L. Ibánez, (World Scienti.c, Singapore, 1985), p. 147; P. Breitenlohner, D. Maison, G. W. Gibbons: Commun. Math. Phys. 120, 295 (1988); R. Kallosh, A. D. Linde, T. Ortin, A. W. Peet, A. Van Proeyen: Phys. Rev. D 46, 5278 (1992); R. Kallosh, T. Ortin, A. W. Peet: Phys. Rev. D 47, 5400 (1993); R. Kallosh: Phys. Lett. B 282, 80 (1992); R. Kallosh, A. W. Peet: Phys. Rev. D 46, 5223 (1992); R. R. Khuri, T. Ortin: Nucl. Phys. B 467, 355 (1996); A. Sen: Nucl. Phys. B 440, 421 (1995); A. Sen: Phys. Lett. B 303, 22 (1993); A. Sen: Mod. Phys. Lett. A 10, 2081 (1995); M. Cvetic, C. M. Hull: Nucl. Phys. B 480, 296 (1996); M. Cvetic, I. Gaida: Nucl. Phys. B 505, 291 (1997); M. Cvetic, D. Youm: arXiv:hepth/9512127; M. Cvetic, A. A. Tseytlin: Phys. Rev. D 53, 5619 (1996)

    Google Scholar 

  6. For reviews on black holes in superstring theory see: J. M. Maldacena: Black-Holes in String Theory, hep-th/9607235; A. W. Peet: TASI lectures on black holes in string theory, arXiv:hep-th/0008241; B. Pioline: Class. Quant. Grav. 23, S981 (2006); A. Dabholkar: Class. Quant. Grav. 23, S957 (2006)

    Google Scholar 

  7. S. W. Hawking: Phys. Rev. Lett. 26, 1344 (1971); J. D. Bekenstein: Phys. Rev. D 7, 2333 (1973)

    Article  ADS  Google Scholar 

  8. A. Strominger, C. Vafa: Phys. Lett. B 379, 99 (1996); C. G. . Callan, J. M. Maldacena: Nucl. Phys. B 472, 591 (1996); G. T. Horowitz, A. Strominger: Phys. Rev. Lett. 77, 2368 (1996); R. Dijkgraaf, E. P. Verlinde, H. L. Verlinde: Nucl. Phys. B 486, 77 (1997); D. M. Kaplan, D. A. Lowe, J. M. Maldacena, A. Strominger: Phys. Rev. D 55, 4898 (1997); J. M. Maldacena: Phys. Lett. B 403, 20 (1997); J. M. Maldacena, A. Strominger, E. Witten: JHEP 9712, 002 (1997); M. Bertolini, M. Trigiante: JHEP 0010, 002 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  9. E. Witten: Nucl. Phys. B 443, 85 (1995)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  10. C. M. Hull, P. K. Townsend: Nucl. Phys. B 438, 109 (1995)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  11. G. Nordstrüom: Proc. Kon. Ned. Akad. Wet. 20, 1238 (1918); H. Reissner: Ann. Physik 50, 106 (1916)

    ADS  Google Scholar 

  12. R. Penrose: Riv. Nuovo Cim. 1, 252 (1969); Gen. Rel. Grav. 34, 1141 (2002); R. Penrose: in General Relativity, an Einstein Centenary Survey,ed. by S. W. Hawking, W. Israel (Cambridge University Press, Cambridge, 1979)

    ADS  Google Scholar 

  13. B. Bertotti: Phys. Rev. 116, 1331 (1959); I. Robinson: Bull. Acad. Pol. Sci. Ser. Sci. Math. Astron. Phys. 7, 351 (1959)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  14. R. Kallosh, T. Ortin: Phys. Rev. D 48, 742 (1993); E. Bergshoe., R. Kallosh, T. Ortin: Nucl. Phys. B 478, 156 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  15. The literature on this topic is quite extended. As a general review, see the lecture notes: K. Stelle: Lectures on Supergravity p-Branes, presented at 1996 ICTP Summer School, Trieste, arXiv:hep-th/9701088

    Google Scholar 

  16. M. J. Du., R. R. Khuri, J. X. Lu: String solitons, Phys. Rep. 259, 213 (1995)

    ADS  Google Scholar 

  17. For recent reviews see: J. H. Schwarz: Nucl. Phys. Proc. Suppl. B 55, 1 (1997); M. J. Du.: Int. J. Mod. Phys. A 11, 5623 (1996); A. Sen: Nucl. Phys. Proc. Suppl. 58, 5 (1997)

    Google Scholar 

  18. J. H. Schwarz, A. Sen, Phys. Lett. B 312, 105 (1993); J. H. Schwarz, A. Sen: Nucl. Phys. B 411, 35 (1994)

    Google Scholar 

  19. M. Gasperini, J. Maharana, G. Veneziano: Phys. Lett. B 272, 277 (1991); J. Maharana, J. H. Schwarz: Nucl. Phys. B 390, 3 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  20. J. H. Schwarz: M theory extensions of T duality, arXiv:hep-th/9601077; C. Vafa: Nucl. Phys. B 469, 403 (1996)

    Article  Google Scholar 

  21. S. Ferrara, R. Kallosh, A. Strominger: Phys. Rev. D 52, 5412 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  22. S. Ferrara, R. Kallosh: Phys. Rev. D 54, 1514 (1996); S. Ferrara, R. Kallosh: Phys. Rev. D 54, 1525 (1996)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. A. Strominger: Phys. Lett. B 383, 39 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  24. J. Polchinski, Y. Cai: Nucl. Phys. B 296, 91 (1988); C. G. . Callan, C. Lovelace, C. R. Nappi, S. A. Yost: Nucl. Phys. B 308, 221 (1988); A. Sagnotti: Open strings and their symmetry groups, Cargese Summer Inst. (1987) 0521, arXiv:hep-th/0208020; M. Bianchi, A. Sagnotti: Phys. Lett. B 247, 517 (1990); M. Bianchi, A. Sagnotti: Nucl. Phys. B 361, 519 (1991); P. Horava: Nucl. Phys. B 327, 461 (1989); J. Polchinski: Phys. Rev. Lett. 75, 4724 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  25. S. Ferrara, J. M. Maldacena: Class. Quant. Grav. 15, 749 (1998); S. Ferrara, M. Gunaydin: Int. J. Mod. Phys. A 13, 2075 (1998) 726 L. Andrianopoli et al.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  26. L. Andrianopoli, R. D’Auria, S. Ferrara: Phys. Lett. B 403, 12 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  27. R. M. Wald: Phys. Rev. D 48, 3427 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  28. G. Lopes Cardoso, B. de Wit, T. Mohaupt: Phys. Lett. B 451, 309 (1999); G. Lopes Cardoso, B. de Wit, T. Mohaupt: Nucl. Phys. B 567, ) 87 (2000)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  29. H. Ooguri, A. Strominger, C. Vafa: Phys. Rev. D 70, 106007 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  30. R. R. Khuri, T. Ortin: Phys. Lett. B 373, 56 (1996); T. Ortin: Phys. Lett. B 422, 93 (1998); T. Ortin: Non-supersymmetric (but) extreme black holes, scalar hair and other open problems, arXiv:hep-th/9705095

    Article  ADS  MathSciNet  Google Scholar 

  31. S. Ferrara, G. W. Gibbons, R. Kallosh: Nucl. Phys. B 500, 75 (1997)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  32. K. Goldstein, N. Iizuka, R. P. Jena, S. P. Trivedi: Phys. Rev. D 72, 124021 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  33. R. Kallosh: JHEP 0512, 022 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  34. P. K. Tripathy, S. P. Trivedi: JHEP 0603, 022 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  35. A. Giryavets: JHEP 0603, 020 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  36. R. Kallosh, N. Sivanandam, M. Soroush: JHEP 0603, 060 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  37. A. Dabholkar, A. Sen, S. Trivedi: Black hole microstates and attractor without supersymmetry, arXiv:hep-th/0611143

    Google Scholar 

  38. G. G. Gibbons: http://www.lpthe.jussieu.fr/sugra30/TALKS/Gibbons.pdf, talk presented at the conference 30 years of Supergravity, journée Joüel Scherk, held in Paris the 18/10/2006

    Google Scholar 

  39. M. K. Gaillard, B. Zumino: Nucl. Phys. B 193, 221 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  40. R. Kallosh: From BPS to non-BPS black holes canonically, arXiv:hepth/0603003

    Google Scholar 

  41. For a review, see for instance: S. Bellucci, S. Ferrara, A. Marrani: Supersymmetric Mechanics P Vol. 2: The Attractor Mechanism and Space Time Singularities, Lecture Notes in Physics, Vol. 701 (Springer, Berlin/Heidelberg, 2006), Proceedings of the SSM05–Winter School on Modern Trends in supersymmetric Mechanics, INFN-LNF, Italy (2005)

    Google Scholar 

  42. G. Lopes Cardoso, B. de Wit, J. Kappeli, T. Mohaupt: JHEP 0412, 075 (2004)

    ADS  Google Scholar 

  43. A. Sen: JHEP 0509, 038 (2005)

    Article  ADS  Google Scholar 

  44. L. Andrianopoli, R. D’Auria, S. Ferrara, M. A. Lledo: Nucl. Phys. B 640, 46 (2002)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  45. B. Zumino: J.Math.Phys. 3, 1055 (1962)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  46. E. Witten, D. I. Olive: Phys. Lett. B 78, 97 (1978)

    Article  ADS  Google Scholar 

  47. For a review on supergravity see for example: L. Castellani, R. D’Auria, P. Fré, Supergravity and Superstring Theory: A Geometric Perspective(World Scienti .c, Singapore, 1990)

    Google Scholar 

  48. E. Cremmer: in Supergravity ’81, ed. by S. Ferrara, J. G. Taylor, p. 313; B. Julia: in Superspace & Supergravity, ed. by S. Hawking, M. Rocek (Cambridge, 1981) p. 331

    Google Scholar 

  49. A. Salam, E. Sezgin: Supergravities in Diverse Dimensions, ed. by A. Salam, E. Sezgin (North-Holland, World Scienti.c, 1989), Vol. 1

    Google Scholar 

  50. L. Andrianopoli, R. D’Auria, S. Ferrara: Int. J. Mod. Phys. A 13, 431 (1998)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  51. L. Andrianopoli, R. D’Auria, S. Ferrara: Int. J. Mod. Phys. A 12, 3759 (1997)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  52. L. Castellani, A. Ceresole, S. Ferrara, R. D’Auria, P. Fré, E. Maina: Nucl. Phys. B 268, 317 (1986)

    Article  ADS  Google Scholar 

  53. E. Bergshoe., I. G. Koh, E. Sezgin: Phys. Lett. B 155, 71 (1985); M. de Roo, P. Wagemans: Nucl. Phys. B 262, 644 (1985)

    Article  ADS  Google Scholar 

  54. S. Ferrara, R. Kallosh: Phys. Rev. D 73, 125005 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  55. S. Ferrara, A. Strominger: in Proceedings of College Station Workshop Strings ‘89’, ed. by Arnowitt et al. (World Scienti.c, Singapore, 1989), p. 245; P. Candelas, X. de la Ossa: Nucl. Phys. B 355, 455 (1991); B. de Wit, A. Van Proeyen: Nucl. Phys. B 245, 89 (1984); E. Cremmer, C. Kounnas, A. Van Proeyen, J. P. Derendinger, S. Ferrara, B. de Wit, L. Girardello: Nucl. Phys. B 250, 385 (1985); B. de Wit, P. G. Lauwers, A. Van Proeyen: Nucl. Phys. B 255, 569 (1985); S. Ferrara, C. Kounnas, D. Lust, F. Zwirner: Nucl. Phys. B 365, 431 (1991); L. Castellani, R. D’Auria, S. Ferrara: Class. Quant. Grav. 7, 1767 (1990); L. Castellani, R. D’Auria, S. Ferrara: Phys. Lett. B 241, 57 (1990)

    Google Scholar 

  56. A. Strominger: Commun. Math. Phys. 133, 163 (1990)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  57. L. Andrianopoli, M. Bertolini, A. Ceresole, R. D’Auria, S. Ferrara, P. Fré, T. Magri: J. Geom. Phys. 23, 111 (1997); L. Andrianopoli, M. Bertolini, A. Ceresole, R. D’Auria, S. Ferrara, P. Fré: Nucl. Phys. B 476, 397 (1996)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  58. E. Cremmer, A. Van Proeyen: Class. Quant. Grav. 2, 445 (1985)

    Article  MATH  ADS  Google Scholar 

  59. L. Andrianopoli, R. D’Auria, S. Ferrara, P. Fre, M. Trigiante: Nucl. Phys. B 509, 463 (1998); G. Arcioni, A. Ceresole, F. Cordaro, R. D’Auria, P. Fre, L. Gualtieri, M. Trigiante: Nucl. Phys. B 542, 273 (1999)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  60. K. Behrndt, D. Lust, W. A. Sabra: Nucl. Phys. B 510, 264 (1998)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  61. P. Meessen, T. Ortin: Nucl. Phys. B 749, ) 291 (2006)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  62. P. Fré: Nucl. Phys. Proc. Suppl. 57, 52 (1997)

    Article  MATH  ADS  Google Scholar 

  63. M. Alishahiha, H. Ebrahim: JHEP 0603, 003 (2006); M. Alishahiha, H. Ebrahim: JHEP 0611, 017 (2006)

    Article  MathSciNet  Google Scholar 

  64. P. Kaura, A. Misra: On the existence of non-supersymmetric black hole attractors for two-parameter Calabi-Yau’s and attractor equations, arXiv:hepth/0607132

    Google Scholar 

  65. S. Bellucci, S. Ferrara, A. Marrani, A. Yeranyan: Mirror Fermat Calabi-Yau threefolds and Landau-Ginzburg black hole attractors, arXiv:hep-th/0608091

    Google Scholar 

  66. D. Astefanesei, K. Goldstein, S. Mahapatra: Moduli and (un)attractor black hole thermodynamics, arXiv:hep-th/0611140

    Google Scholar 

  67. G. W. Gibbons, R. Kallosh, B. Kol: Phys. Rev. Lett. 77, 4992 (1996)

    Article  ADS  Google Scholar 

  68. S. Ferrara, C. A. Savoy, B. Zumino: Phys. Lett. B 100, 393 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  69. A. Ceresole, R. D’Auria, S. Ferrara: Nucl. Phys. Proc. Suppl. 46, 67 (1996)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  70. R. Kallosh, B. Kol: Phys. Rev. D 53, 5344 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  71. S. Ferrara, E. G. Gimon, R. Kallosh: Magic supergravities, N = 8 and black-hole composites, arXiv:hep-th/0606211

    Google Scholar 

  72. M. Gunaydin, O. Pavlyk: JHEP 0508, 101 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  73. S. Bellucci, S. Ferrara, A. Marrani: Phys. Lett. B 635, 172 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  74. S. Ferrara, M. Bodner, A. C. Cadavid: Phys. Lett. B 247, 25 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  75. S. Bellucci, S. Ferrara, M. Gunaydin, A. Marrani: Int. J. Mod. Phys. A 21, 5043 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  76. E. Cremmer, A. Van Proeyen: Class. Quant. Grav. 2, 445 (1985)

    Article  MATH  ADS  Google Scholar 

  77. B. de Wit, F. Vanderseypen, A. Van Proeyen: Nucl. Phys. B 400, 463 (1993)

    Article  MATH  ADS  Google Scholar 

  78. M. R. Douglas: JHEP 0305, 046 (2003); F. Denef, M. R. Douglas: Computational complexity of the landscape. I, arXiv:hep-th/0602072

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Andrianopoli, L., D’Auria, R., Ferrara, S., Trigiante, M. (2008). Extremal Black Holes in Supergravity. In: Gasperini, M., Maharana, J. (eds) String Theory and Fundamental Interactions. Lecture Notes in Physics, vol 737. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74233-3_22

Download citation

Publish with us

Policies and ethics