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Black Holes, Black Rings, and their Microstates

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Supersymmetric Mechanics - Vol. 3

Part of the book series: Lecture Notes in Physics ((LNP,volume 755))

Abstract

In this review article, we describe some of the recent progress towards the construction and analysis of three-charge configurations in string theory and supergravity. We begin by describing the Born-Infeld construction of three-charge supertubes with two dipole charges and then discuss the general method of constructing three-charge solutions in five dimensions. We explain in detail the use of these methods to construct black rings, black holes, as well as smooth microstate geometries with black hole and black ring charges, but with no horizon. We present arguments that many of these microstate geometries are dual to boundary states that belong to the same sector of the D1-D5-P CFT as the typical states. We end with an extended discussion of the implications of this work for the physics of black holes in string theory.

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References

  1. S. W. Hawking, “Breakdown of predictability in gravitational collapse,” Phys. Rev. D 14, 2460 (1976).

    Article  ADS  MathSciNet  Google Scholar 

  2. S. W. Hawking, “Particle creation by black holes,” Commun. Math. Phys. 43, 199 (1975) [Erratum-ibid. 46, 206 (1976)].

    Article  MathSciNet  ADS  Google Scholar 

  3. A. Strominger and C. Vafa, “Microscopic origin of the bekenstein-Hawking entropy,” Phys. Lett. B 379, 99 (1996) [arXiv:hep-th/9601029].

    Article  ADS  MathSciNet  Google Scholar 

  4. J. M. Maldacena, “The large N limit of superconformal field theories and supergravity,” Adv. Theor. Math. Phys. 2, 231 (1998) [Int. J. Theor. Phys. 38, 1113 (1999)] [arXiv:hep-th/9711200].

    MATH  ADS  MathSciNet  Google Scholar 

  5. S. S. Gubser, I. R. Klebanov and A. M. Polyakov, “Gauge theory correlators from non-critical string theory,” Phys. Lett. B 428, 105 (1998) [arXiv:hep-th/9802109].

    Article  MathSciNet  ADS  Google Scholar 

  6. E. Witten, “Anti-de Sitter space and holography,” Adv. Theor. Math. Phys. 2, 253 (1998) [arXiv:hep-th/9802150].

    MATH  MathSciNet  Google Scholar 

  7. M. Cvetic and A. A. Tseytlin, “Solitonic strings and BPS saturated dyonic black holes,” Phys. Rev. D 53, 5619 (1996) [arXiv:hep-th/9512031].

    Article  ADS  MathSciNet  Google Scholar 

  8. M. Cvetic and D. Youm, “Dyonic BPS saturated black holes of heterotic string on a six torus,” Phys. Rev. D 53, 584 (1996) [arXiv:hep-th/9507090].

    Article  ADS  MathSciNet  Google Scholar 

  9. O. Lunin and S. D. Mathur, “AdS/CFT duality and the black hole information paradox,” Nucl. Phys. B 623, 342 (2002) [arXiv:hep-th/0109154].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  10. O. Lunin and S. D. Mathur, “Statistical interpretation of Bekenstein entropy for systems with a stretched horizon,” Phys. Rev. Lett. 88, 211303 (2002) [arXiv:hep-th/0202072].

    Article  ADS  MathSciNet  Google Scholar 

  11. O. Lunin, J. M. Maldacena and L. Maoz, “Gravity solutions for the D1-D5 system with angular momentum,” arXiv:hep-th/0212210.

    Google Scholar 

  12. O. Lunin and S. D. Mathur, “The slowly rotating near extremal D1-D5 system as a ‘hot tube’,” Nucl. Phys. B 615, 285 (2001) [arXiv:hep-th/0107113].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  13. L. F. Alday, J. de Boer and I. Messamah, “The gravitational description of coarse grained microstates,” arXiv:hep-th/0607222.

    Google Scholar 

  14. A. Donos and A. Jevicki, “Dynamics of chiral primaries in AdS(3) x S**3 x T**4,” Phys. Rev. D 73, 085010 (2006) [arXiv:hep-th/0512017].

    Article  ADS  Google Scholar 

  15. L. F. Alday, J. de Boer and I. Messamah, “What is the dual of a dipole?,” Nucl. Phys. B 746, 29 (2006) [arXiv:hep-th/0511246].

    Article  MATH  ADS  Google Scholar 

  16. S. Giusto, S. D. Mathur and Y. K. Srivastava, “Dynamics of supertubes,” Nucl. Phys. B 754, 233 (2006) [arXiv:hep-th/0510235].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  17. M. Taylor, “General 2 charge geometries,” JHEP 0603, 009 (2006) [arXiv:hep-th/0507223].

    Article  ADS  Google Scholar 

  18. K. Skenderis and M. Taylor, “Fuzzball solutions and D1-D5 microstates,” arXiv:hep-th/0609154.

    Google Scholar 

  19. N. Iizuka and M. Shigemori, “A note on D1-D5-J system and 5D small black ring,” JHEP 0508, 100 (2005) [arXiv:hep-th/0506215].

    Article  ADS  MathSciNet  Google Scholar 

  20. M. Boni and P. J. Silva, “Revisiting the D1/D5 system or bubbling in AdS(3),” JHEP 0510, 070 (2005) [arXiv:hep-th/0506085].

    Article  ADS  MathSciNet  Google Scholar 

  21. D. Martelli and J. F. Morales, “Bubbling AdS(3),” JHEP 0502, 048 (2005) [arXiv:hep-th/0412136].

    Article  ADS  MathSciNet  Google Scholar 

  22. Y. K. Srivastava, “Bound states of KK monopole and momentum,” arXiv:hep-th/0611124.

    Google Scholar 

  23. V. Balasubramanian, P. Kraus and M. Shigemori, “Massless black holes and black rings as effective geometries of the D1-D5 system,” Class. Quant. Grav. 22, 4803 (2005) [arXiv:hep-th/0508110].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  24. I. Kanitscheider, K. Skenderis and M. Taylor, “Holographic anatomy of fuzzballs,” arXiv:hep-th/0611171.

    Google Scholar 

  25. A. A. Tseytlin, “Extreme dyonic black holes in string theory,” Mod. Phys. Lett. A 11, 689 (1996) [arXiv:hep-th/9601177].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  26. A. A. Tseytlin, “Extremal black hole entropy from conformal string sigma model,” Nucl. Phys. B 477, 431 (1996) [arXiv:hep-th/9605091].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  27. S. D. Mathur, “The fuzzball proposal for black holes: An elementary review,” Fortsch. Phys. 53, 793 (2005) [arXiv:hep-th/0502050].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  28. S. D. Mathur, “The quantum structure of black holes,” Class. Quant. Grav. 23, R115 (2006) [arXiv:hep-th/0510180].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  29. B. C. Palmer and D. Marolf, “Counting supertubes,” JHEP 0406, 028 (2004) [arXiv:hep-th/0403025].

    Article  Google Scholar 

  30. V. S. Rychkov, “D1-D5 black hole microstate counting from supergravity,” JHEP 0601, 063 (2006) [arXiv:hep-th/0512053].

    Article  ADS  MathSciNet  Google Scholar 

  31. D. Bak, Y. Hyakutake and N. Ohta, “Phase moduli space of supertubes,” Nucl. Phys. B 696, 251 (2004) [arXiv:hep-th/0404104].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  32. D. Bak, Y. Hyakutake, S. Kim and N. Ohta, “A geometric look on the microstates of supertubes,” Nucl. Phys. B 712, 115 (2005) [arXiv:hep-th/0407253].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  33. D. Mateos and P. K. Townsend, “Supertubes,” Phys. Rev. Lett. 87, 011602 (2001) [arXiv:hep-th/0103030].

    Article  ADS  MathSciNet  Google Scholar 

  34. D. Mateos, S. Ng and P. K. Townsend, “Supercurves,” Phys. Lett. B 538, 366 (2002) [arXiv:hep-th/0204062].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  35. R. Emparan, D. Mateos and P. K. Townsend, “Supergravity supertubes,” JHEP 0107, 011 (2001) [arXiv:hep-th/0106012].

    Article  ADS  MathSciNet  Google Scholar 

  36. O. Lunin and S. D. Mathur, “Metric of the multiply wound rotating string,” Nucl. Phys. B 610, 49 (2001) [arXiv:hep-th/0105136].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  37. A. Sen, “Extremal black holes and elementary string states,” Mod. Phys. Lett. A 10, 2081 (1995) [arXiv:hep-th/9504147].

    Article  ADS  Google Scholar 

  38. I. Bena and P. Kraus, “Three charge supertubes and black hole hair,” Phys. Rev. D 70, 046003 (2004) [arXiv:hep-th/0402144].

    Article  ADS  MathSciNet  Google Scholar 

  39. J. R. David, G. Mandal and S. R. Wadia, “Microscopic formulation of black holes in string theory,” Phys. Rept. 369, 549 (2002) [arXiv:hep-th/0203048].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  40. O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri and Y. Oz, “Large N field theories, string theory and gravity,” Phys. Rept. 323, 183 (2000) [arXiv:hep-th/9905111].

    Article  ADS  MathSciNet  Google Scholar 

  41. S. Giusto, S. D. Mathur and A. Saxena, “Dual geometries for a set of 3-charge microstates,” Nucl. Phys. B 701, 357 (2004) [arXiv:hep-th/0405017].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  42. S. Giusto, S. D. Mathur and A. Saxena, “3-charge geometries and their CFT duals,” Nucl. Phys. B 710, 425 (2005) [arXiv:hep-th/0406103].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  43. S. Giusto and S. D. Mathur, “Geometry of D1-D5-P bound states,” Nucl. Phys. B 729, 203 (2005) [arXiv:hep-th/0409067].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  44. S. Giusto, S. D. Mathur and Y. K. Srivastava, “A microstate for the 3-charge black ring,” arXiv:hep-th/0601193.

    Google Scholar 

  45. O. Lunin, “Adding momentum to D1-D5 system,” JHEP 0404, 054 (2004) [arXiv:hep-th/0404006].

    Article  ADS  MathSciNet  Google Scholar 

  46. I. Bena and P. Kraus, “Microstates of the D1-D5-KK system,” Phys. Rev. D 72, 025007 (2005) [arXiv:hep-th/0503053].

    Article  ADS  MathSciNet  Google Scholar 

  47. I. Bena and N. P. Warner, “Bubbling supertubes and foaming black holes,” Phys. Rev. D 74, 066001 (2006) [arXiv:hep-th/0505166].

    Article  ADS  MathSciNet  Google Scholar 

  48. P. Berglund, E. G. Gimon and T. S. Levi, “Supergravity microstates for BPS black holes and black rings,” JHEP 0606, 007 (2006) [arXiv:hep-th/0505167].

    Article  ADS  MathSciNet  Google Scholar 

  49. A. Saxena, G. Potvin, S. Giusto and A. W. Peet, “Smooth geometries with four charges in four dimensions,” JHEP 0604 (2006) 010 [arXiv:hep-th/0509214].

    Article  ADS  MathSciNet  Google Scholar 

  50. S. Giusto, S. D. Mathur and Y. K. Srivastava, “A microstate for the 3-charge black ring,” arXiv:hep-th/0601193.

    Google Scholar 

  51. I. Bena, C. W. Wang and N. P. Warner, “The foaming three-charge black hole,” arXiv:hep-th/0604110.

    Google Scholar 

  52. V. Balasubramanian, E. G. Gimon and T. S. Levi, “Four dimensional black hole microstates: From D-branes to spacetime foam,” arXiv:hep-th/0606118.

    Google Scholar 

  53. I. Bena, C. W. Wang and N. P. Warner, “Mergers and typical black hole microstates,” JHEP 0611, 042 (2006) [arXiv:hep-th/0608217].

    Article  ADS  MathSciNet  Google Scholar 

  54. M. C. N. Cheng, “More bubbling solutions,” arXiv:hep-th/0611156.

    Google Scholar 

  55. J. Ford, S. Giusto and A. Saxena, “A class of BPS time-dependent 3-charge microstates from spectral flow,” arXiv:hep-th/0612227.

    Google Scholar 

  56. I. Bena and P. Kraus, “Microscopic description of black rings in AdS/CFT,” JHEP 0412, 070 (2004) [arXiv:hep-th/0408186].

    Article  ADS  MathSciNet  Google Scholar 

  57. A. Dabholkar, “Exact counting of black hole microstates,” Phys. Rev. Lett. 94, 241301 (2005) [arXiv:hep-th/0409148].

    Article  ADS  MathSciNet  Google Scholar 

  58. S. Ferrara and R. Kallosh, “Supersymmetry and attractors,” Phys. Rev. D 54, 1514 (1996) [arXiv:hep-th/9602136].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  59. H. Ooguri, A. Strominger and C. Vafa, “Black hole attractors and the topological string,” Phys. Rev. D 70, 106007 (2004) [arXiv:hep-th/0405146].

    Article  ADS  MathSciNet  Google Scholar 

  60. P. Kraus, “Lectures on black holes and the AdS(3)/CFT(2) correspondence,” arXiv:hep-th/0609074.

    Google Scholar 

  61. B. Pioline, “Lectures on on black holes, topological strings and quantum attractors,” Class. Quant. Grav. 23, S981 (2006) [arXiv:hep-th/0607227].

    Article  ADS  MathSciNet  Google Scholar 

  62. A. Sen, “How does a fundamental string stretch its horizon?,” JHEP 0505, 059 (2005) [arXiv:hep-th/0411255].

    Article  ADS  Google Scholar 

  63. A. Dabholkar, F. Denef, G. W. Moore and B. Pioline, “Precision counting of small black holes,” JHEP 0510, 096 (2005) [arXiv:hep-th/0507014].

    Article  ADS  MathSciNet  Google Scholar 

  64. A. Dabholkar, F. Denef, G. W. Moore and B. Pioline, “Exact and asymptotic degeneracies of small black holes,” JHEP 0508, 021 (2005) [arXiv:hep-th/0502157].

    Article  ADS  MathSciNet  Google Scholar 

  65. A. Dabholkar, N. Iizuka, A. Iqubal, A. Sen and M. Shigemori, “Spinning strings as small black rings,” arXiv:hep-th/0611166.

    Google Scholar 

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

    Google Scholar 

  67. J. Polchinski and M. J. Strassler, “The string dual of a confining four-dimensional gauge theory,” arXiv:hep-th/0003136.

    Google Scholar 

  68. I. Bena and N. P. Warner, “One ring to rule them all æ and in the darkness bind them?,” Adv. Theor. Math. Phys. 9 (2005) 667–701 [arXiv:hep-th/0408106.]

    MATH  MathSciNet  Google Scholar 

  69. I. Bena, C. W. Wang and N. P. Warner, “Black rings with varying charge density,” JHEP 0603, 015 (2006) [arXiv:hep-th/0411072].

    Article  ADS  MathSciNet  Google Scholar 

  70. W. I. Taylor, “Adhering 0-branes to 6-branes and 8-branes,” Nucl. Phys. B 508, 122 (1997) [arXiv:hep-th/9705116].

    Article  MATH  Google Scholar 

  71. I. Bena, “Splitting hairs of the three charge black hole,” Phys. Rev. D 70, 105018 (2004) [arXiv:hep-th/0404073].

    Article  ADS  MathSciNet  Google Scholar 

  72. J. D. Jackson, Classical Electrodynamics, Wiley, New York, NY, 1975.

    MATH  Google Scholar 

  73. J. C. Breckenridge, R. C. Myers, A. W. Peet and C. Vafa, “D-branes and spinning black holes,” Phys. Lett. B 391, 93 (1997) [arXiv:hep-th/9602065].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  74. C. A. R. Herdeiro, “Special properties of five dimensional BPS rotating black holes,” Nucl. Phys. B 582, 363 (2000) [arXiv:hep-th/0003063].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  75. G. T. Horowitz and J. Polchinski, “A correspondence principle for black holes and strings,” Phys. Rev. D 55, 6189 (1997) [arXiv:hep-th/9612146].

    Article  ADS  MathSciNet  Google Scholar 

  76. H. S. Reall, “Higher dimensional black holes and supersymmetry,” Phys. Rev. D 68, 024024 (2003) [arXiv:hep-th/0211290].

    Article  ADS  MathSciNet  Google Scholar 

  77. H. Elvang, R. Emparan, D. Mateos and H. S. Reall, “A supersymmetric black ring,” Phys. Rev. Lett. 93, 211302 (2004) [arXiv:hep-th/0407065].

    Article  ADS  MathSciNet  Google Scholar 

  78. H. Elvang, R. Emparan, D. Mateos and H. S. Reall, “Supersymmetric black rings and three-charge supertubes,” Phys. Rev. D 71, 024033 (2005) [arXiv:hep-th/0408120].

    Article  ADS  MathSciNet  Google Scholar 

  79. J. P. Gauntlett and J. B. Gutowski, “General concentric black rings,” Phys. Rev. D 71, 045002 (2005) [arXiv:hep-th/0408122].

    Article  ADS  MathSciNet  Google Scholar 

  80. S. W. Hawking, “Gravitational Instantons,” Phys. Lett. A 60, 81 (1977).

    Article  MathSciNet  ADS  Google Scholar 

  81. D. Gaiotto, A. Strominger and X. Yin, “New connections between 4D and 5D black holes,” JHEP 0602, 024 (2006) [arXiv:hep-th/0503217].

    Article  ADS  MathSciNet  Google Scholar 

  82. D. Gaiotto, A. Strominger and X. Yin, “5D black rings and 4D black holes,” JHEP 0602, 023 (2006) [arXiv:hep-th/0504126].

    Article  ADS  MathSciNet  Google Scholar 

  83. H. Elvang, R. Emparan, D. Mateos and H. S. Reall, “Supersymmetric 4D rotating black holes from 5D black rings,” JHEP 0508, 042 (2005) [arXiv:hep-th/0504125].

    Article  ADS  MathSciNet  Google Scholar 

  84. I. Bena, P. Kraus and N. P. Warner, “Black rings in Taub-NUT,” Phys. Rev. D 72, 084019 (2005) [arXiv:hep-th/0504142].

    Article  ADS  MathSciNet  Google Scholar 

  85. I. R. Klebanov and A. A. Tseytlin, “Gravity duals of supersymmetric SU(N) x SU(N+M) gauge theories,” Nucl. Phys. B 578, 123 (2000) [arXiv:hep-th/0002159].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  86. I. R. Klebanov and M. J. Strassler, “Supergravity and a confining gauge theory: Duality cascades and χSB-resolution of naked singularities,” JHEP 0008, 052 (2000) [arXiv:hep-th/0007191].

    Article  ADS  MathSciNet  Google Scholar 

  87. A. W. Peet, “TASI lectures on black holes in string theory,” arXiv:hep-th/0008241.

    Google Scholar 

  88. R. Emparan and H. S. Reall, “Black rings,” Class. Quant. Grav. 23, R169 (2006) [arXiv:hep-th/0608012].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  89. H. Elvang and P. Figueras, “Black Saturn,” arXiv:hep-th/0701035.

    Google Scholar 

  90. R. Emparan and H. S. Reall, “A rotating black ring in five dimensions,” Phys. Rev. Lett. 88, 101101 (2002) [arXiv:hep-th/0110260].

    Article  ADS  MathSciNet  Google Scholar 

  91. R. Emparan, “Rotating circular strings, and infinite non-uniqueness of black rings,” JHEP 0403, 064 (2004) [arXiv:hep-th/0402149].

    Article  ADS  MathSciNet  Google Scholar 

  92. H. Elvang and R. Emparan, “Black rings, supertubes, and a stringy resolution of black hole non-uniqueness,” JHEP 0311, 035 (2003) [arXiv:hep-th/0310008].

    Article  ADS  MathSciNet  Google Scholar 

  93. I. Bena, C. W. Wang and N. P. Warner, “Sliding rings and spinning holes,” JHEP 0605, 075 (2006) [arXiv:hep-th/0512157].

    Article  ADS  MathSciNet  Google Scholar 

  94. G. W. Gibbons and S. W. Hawking, “Gravitational Multi - Instantons,” Phys. Lett. B 78, 430 (1978).

    Article  ADS  Google Scholar 

  95. G. W. Gibbons and P. J. Ruback, “The Hidden Symmetries of Multi-Center Metrics,” Commun. Math. Phys. 115, 267 (1988).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  96. J. P. Gauntlett, J. B. Gutowski, C. M. Hull, S. Pakis and H. S. Reall, “All supersymmetric solutions of minimal supergravity in five dimensions,” Class. Quant. Grav. 20, 4587 (2003) [arXiv:hep-th/0209114].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  97. R. Kallosh and B. Kol, “E(7) Symmetric Area of the Black Hole Horizon,” Phys. Rev. D 53, 5344 (1996) [arXiv:hep-th/9602014].

    Article  ADS  MathSciNet  Google Scholar 

  98. F. Denef, “Supergravity flows and D-brane stability,” JHEP 0008, 050 (2000) [arXiv:hep-th/0005049].

    Article  ADS  MathSciNet  Google Scholar 

  99. B. Bates and F. Denef, “Exact solutions for supersymmetric stationary black hole composites,” arXiv:hep-th/0304094.

    Google Scholar 

  100. F. Denef, “Quantum quivers and Hall/hole halos,” JHEP 0210, 023 (2002) [arXiv:hep-th/0206072].

    Article  ADS  MathSciNet  Google Scholar 

  101. K. Behrndt, G. Lopes Cardoso and S. Mahapatra, “Exploring the relation between 4D and 5D BPS solutions,” Nucl. Phys. B 732, 200 (2006) [arXiv:hep-th/0506251].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  102. S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time, Cambridge University Press, Cambridge, 1975.

    Google Scholar 

  103. V. Jejjala, O. Madden, S. F. Ross and G. Titchener, “Non-supersymmetric smooth geometries and D1-D5-P bound states,” Phys. Rev. D 71, 124030 (2005) [arXiv:hep-th/0504181].

    Article  ADS  MathSciNet  Google Scholar 

  104. V. Cardoso, O. J. C. Dias, J. L. Hovdebo and R. C. Myers, “Instability of non-supersymmetric smooth geometries,” Phys. Rev. D 73, 064031 (2006) [arXiv:hep-th/0512277].

    Article  ADS  MathSciNet  Google Scholar 

  105. J. P. Gauntlett and J. B. Gutowski, “Concentric black rings,” Phys. Rev. D 71, 025013 (2005) [arXiv:hep-th/0408010].

    Article  ADS  MathSciNet  Google Scholar 

  106. M. Cyrier, M. Guica, D. Mateos and A. Strominger, “Microscopic entropy of the black ring,” Phys. Rev. Lett. 94, 191601 (2005) [arXiv:hep-th/0411187].

    Article  ADS  MathSciNet  Google Scholar 

  107. J. M. Maldacena, A. Strominger and E. Witten, “Black hole entropy in M-theory,” JHEP 9712, 002 (1997) [arXiv:hep-th/9711053].

    Article  ADS  MathSciNet  Google Scholar 

  108. M. Bertolini and M. Trigiante, “Microscopic entropy of the most general four-dimensional BPS black hole,” JHEP 0010, 002 (2000) [arXiv:hep-th/0008201].

    Article  ADS  MathSciNet  Google Scholar 

  109. R. Dijkgraaf, J. M. Maldacena, G. W. Moore and E. P. Verlinde, “A black hole farey tail,” arXiv:hep-th/0005003.

    Google Scholar 

  110. P. Kraus and F. Larsen, “Partition functions and elliptic genera from supergravity,” arXiv:hep-th/0607138.

    Google Scholar 

  111. J. de Boer, M. C. N. Cheng, R. Dijkgraaf, J. Manschot and E. Verlinde, “A farey tail for attractor black holes,” JHEP 0611, 024 (2006) [arXiv:hep-th/0608059].

    Article  Google Scholar 

  112. G. T. Horowitz and H. S. Reall, “How hairy can a black ring be?,” Class. Quant. Grav. 22, 1289 (2005) [arXiv:hep-th/0411268].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  113. M. Guica, L. Huang, W. Li and A. Strominger, JHEP 0610, 036 (2006) [arXiv:hep-th/0505188].

    Article  ADS  MathSciNet  Google Scholar 

  114. I. Bena and P. Kraus, “R**2 corrections to black ring entropy,” arXiv:hep-th/0506015.

    Google Scholar 

  115. R. Gopakumar and C. Vafa, “On the gauge theory/geometry correspondence,” Adv. Theor. Math. Phys. 3, 1415 (1999) [arXiv:hep-th/9811131].

    MATH  MathSciNet  Google Scholar 

  116. C. Vafa, “Superstrings and topological strings at large N,” J. Math. Phys. 42, 2798 (2001) [arXiv:hep-th/0008142].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  117. H. Lin, O. Lunin and J. M. Maldacena, “Bubbling AdS space and 1/2 BPS geometries,” JHEP 0410, 025 (2004) [arXiv:hep-th/0409174].

    Article  ADS  MathSciNet  Google Scholar 

  118. F. Cachazo, K. A. Intriligator and C. Vafa, “A large N duality via a geometric transition,” Nucl. Phys. B 603, 3 (2001) [arXiv:hep-th/0103067].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  119. M. Cvetic and F. Larsen, “Near horizon geometry of rotating black holes in five dimensions,” Nucl. Phys. B 531, 239 (1998) [arXiv:hep-th/9805097].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  120. J. M. Maldacena and L. Susskind, “D-branes and fat black holes,” Nucl. Phys. B 475, 679 (1996) [arXiv:hep-th/9604042].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  121. J. McGreevy, L. Susskind and N. Toumbas, “Invasion of the giant gravitons from anti-de Sitter space,” JHEP 0006, 008 (2000) [arXiv:hep-th/0003075].

    Article  ADS  MathSciNet  Google Scholar 

  122. M. T. Grisaru, R. C. Myers and O. Tafjord, “SUSY and Goliath,” JHEP 0008 (2000) 040 [arXiv:hep-th/0008015].

    Google Scholar 

  123. S. R. Das, A. Jevicki and S. D. Mathur, “Giant gravitons, BPS bounds and noncommutativity,” Phys. Rev. D 63, 044001 (2001) [arXiv:hep-th/0008088].

    Article  ADS  MathSciNet  Google Scholar 

  124. A. Hashimoto, S. Hirano and N. Itzhaki, “Large branes in AdS and their field theory dual,” JHEP 0008, 051 (2000) [arXiv:hep-th/0008016].

    Article  ADS  MathSciNet  Google Scholar 

  125. I. Bena and C. Ciocarlie, “Exact N=2 supergravity solutions with polarized branes,” Phys. Rev. D 70, 086005 (2004) [arXiv:hep-th/0212252].

    Article  ADS  MathSciNet  Google Scholar 

  126. I. Bena and R. Roiban, “N=1* in 5 dimensions: Dijkgraaf-Vafa meets Polchinski-Strassler,” JHEP 0311, 001 (2003) [arXiv:hep-th/0308013].

    Article  ADS  MathSciNet  Google Scholar 

  127. Y. K. Srivastava, “Perturbations of supertube in KK monopole background,” arXiv:hep-th/0611320.

    Google Scholar 

  128. A. Saxena, General 3-charge geometries in 4 dimensions (to appear)

    Google Scholar 

  129. S. R. Das and S. D. Mathur, “Excitations of D-strings, entropy and duality,” Phys. Lett. B 375, 103 (1996) [arXiv:hep-th/9601152].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  130. J. M. Maldacena and L. Susskind, “D-branes and fat black holes,” Nucl. Phys. B 475, 679 (1996) [arXiv:hep-th/9604042].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  131. C. G. Callan and J. M. Maldacena, “D-brane Approach to Black Hole Quantum Mechanics,” Nucl. Phys. B 472, 591 (1996) [arXiv:hep-th/9602043].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  132. J. M. Maldacena, “Statistical entropy of near extremal five-branes,” Nucl. Phys. B 477, 168 (1996) [arXiv:hep-th/9605016].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  133. U. H. Danielsson, A. Guijosa and M. Kruczenski, “Brane-antibrane systems at finite temperature and the entropy of black branes,” JHEP 0109, 011 (2001) [arXiv:hep-th/0106201].

    Article  ADS  MathSciNet  Google Scholar 

  134. R. Emparan and G. T. Horowitz, “Microstates of a neutral black hole in M theory,” Phys. Rev. Lett. 97, 141601 (2006) [arXiv:hep-th/0607023].

    Article  ADS  Google Scholar 

  135. B. D. Chowdhury and S. D. Mathur, “Fractional brane state in the early universe,” arXiv:hep-th/0611330.

    Google Scholar 

  136. R. Gregory and R. Laflamme, “Black strings and p-branes are unstable,” Phys. Rev. Lett. 70, 2837 (1993) [arXiv:hep-th/9301052].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  137. T. Harmark, V. Niarchos and N. A. Obers, “Instabilities of black strings and branes,” (Review) arXiv:hep-th/0701022.

    Google Scholar 

  138. B. D. Chowdhury, S. Giusto and S. D. Mathur, “A microscopic model for the black hole - black string phase transition,” arXiv:hep-th/0610069.

    Google Scholar 

  139. T. Harmark, K. R. Kristjansson, N. A. Obers and P. B. Ronne, “Three-charge black holes on a circle,” arXiv:hep-th/0606246.

    Google Scholar 

  140. L. Girardello, M. Petrini, M. Porrati and A. Zaffaroni, “The supergravity dual of N=1 super Yang-Mills theory,” Nucl. Phys. B 569, 451 (2000) [arXiv:hep-th/9909047].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  141. I. Bena and D. J. Smith, “Towards the solution to the giant graviton puzzle,” Phys. Rev. D 71, 025005 (2005) [arXiv:hep-th/0401173].

    Article  ADS  MathSciNet  Google Scholar 

  142. V. Balasubramanian, B. Czech, V. Hubeny, K. Larjo, M. Rangamani and J. Simon, “Typicality versus thermality: An analytic distinction,” arXiv:hep-th/0701122.

    Google Scholar 

  143. V. Balasubramanian, J. de Boer, V. Jejjala and J. Simon, “The library of Babel: On the origin of gravitational thermodynamics,” JHEP 0512, 006 (2005) [arXiv:hep-th/0508023].

    ADS  Google Scholar 

  144. J. M. Maldacena, “Eternal black holes in Anti-de-Sitter,” JHEP 0304, 021 (2003) [arXiv:hep-th/0106112].

    Article  ADS  MathSciNet  Google Scholar 

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

    Google Scholar 

  146. A. Sen, “Black hole entropy function and the attractor mechanism in higher derivative gravity,” JHEP 0509, 038 (2005) [arXiv:hep-th/0506177].

    Article  ADS  Google Scholar 

  147. P. Kraus and F. Larsen, “Holographic gravitational anomalies,” JHEP 0601, 022 (2006) [arXiv:hep-th/0508218].

    Article  ADS  MathSciNet  Google Scholar 

  148. P. Kraus and F. Larsen, “Microscopic black hole entropy in theories with higher derivatives,” JHEP 0509, 034 (2005) [arXiv:hep-th/0506176].

    Article  ADS  MathSciNet  Google Scholar 

  149. S. Giusto and S. D. Mathur, “Fuzzball geometries and higher derivative corrections for extremal holes,” Nucl. Phys. B 738, 48 (2006) [arXiv:hep-th/0412133].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  150. K. Pilch and N. P. Warner, “N=1 supersymmetric renormalization group flows from IIB supergravity,” Adv. Theor. Math. Phys. 4, 627 (2002) [arXiv:hep-th/0006066].

    MathSciNet  Google Scholar 

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  1. Service de Physique Théorique, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, France

    Iosif Bena

  2. Department of Physics and Astronomy, University of Southern California, Los Angeles, CA 90089-0484, USA

    Nicholas P. Warner

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Bena, I., Warner, N.P. (2008). Black Holes, Black Rings, and their Microstates. In: Supersymmetric Mechanics - Vol. 3. Lecture Notes in Physics, vol 755. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79523-0_1

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