Black holes, black rings, and their microstates

Lecture Notes in Physics

Volumn 755, Issue , 2008, Pages 1-92

  Bena, Iosif ^a   Warner, Nicholas P ^b  

^a CEA SACLAY   (France)

^b UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 52649129299     PISSN: 00758450     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-540-79523-0_1     Document Type: Review

References (150)

1. S. W. Hawking, "Breakdown of predictability in gravitational collapse," Phys. Rev. D 14, 2460 (1976). 1
2. S. W. Hawking, "Particle creation by black holes," Commun. Math. Phys. 43, 199 (1975) [Erratum-ibid. 46, 206 (1976)]. 1
3. A. Strominger and C. Vafa, "Microscopic origin of the bekenstein-Hawking entropy," Phys. Lett. B 379, 99 (1996) [arXiv:hep-th/9601029]. 1, 3
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:hepth/9711200]. 2
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]. 2
6. E. Witten, "Anti-de Sitter space and holography," Adv. Theor. Math. Phys. 2, 253 (1998) [arXiv:hep-th/9802150]. 2
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]. 2
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]. 2
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]. 2, 7, 78
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]. 2
11. O. Lunin, J. M. Maldacena and L. Maoz, "Gravity solutions for the D1-D5 system with angular momentum," arXiv:hep-th/0212210. 2, 78, 82
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]. 2, 6
13. L. F. Alday, J. de Boer and I. Messamah, "The gravitational description of coarse grained microstates," arXiv:hep-th/0607222. 2, 6
14. A. Donos and A. Jevicki, "Dynamics of chiral primaries in AdS(3) x S**3 × T**4," Phys. Rev. D 73, 085010 (2006) [arXiv:hep-th/0512017]. 2, 6
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]. 2, 6
16. S. Giusto, S. D. Mathur and Y. K. Srivastava, "Dynamics of supertubes," Nucl. Phys. B 754, 233 (2006) [arXiv:hep-th/ 0510235]. 2, 6
17. M. Taylor, "General 2 charge geometries," JHEP 0603, 009 (2006) [arXiv:hep-th/0507223]. 2, 6
18. K. Skenderis and M. Taylor, "Fuzzball solutions and D1-D5 microstates," arXiv:hepth/0609154. 2, 6
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]. 2, 6
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]. 2, 6
21. D. Martelli and J. F. Morales, "Bubbling AdS(3)," JHEP 0502, 048 (2005) [arXiv:hepth/0412136]. 2, 6
22. Y. K. Srivastava, "Bound states of KK monopole and momentum," arXiv:hep-th/0611124. 2, 6
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:hepth/0508110]. 2, 86
24. I. Kanitscheider, K. Skenderis and M. Taylor, "Holographic anatomy of fuzzballs," arXiv:hep-th/0611171. 2, 6
25. A. A. Tseytlin, "Extreme dyonic black holes in string theory," Mod. Phys. Lett. A 11, 689 (1996) [arXiv:hep-th/9601177]. 2
26. A. A. Tseytlin, "Extremal black hole entropy from conformal string sigma model," Nucl. Phys. B 477, 431 (1996) [arXiv:hep-th/ 9605091]. 2
27. S. D. Mathur, "The fuzzball proposal for black holes: An elementary review," Fortsch. Phys. 53, 793 (2005) [arXiv:hep-th/0502050]. 2, 80, 83
28. S. D. Mathur, "The quantum structure of black holes," Class. Quant. Grav. 23, R115 (2006) [arXiv:hep-th/0510180]. 2, 80, 83
29. B. C. Palmer and D. Marolf, "Counting supertubes," JHEP 0406, 028 (2004) [arXiv:hepth/0403025]. 2, 82
30. V. S. Rychkov, "D1-D5 black hole microstate counting from supergravity," JHEP 0601, 063 (2006) [arXiv:hep-th/0512053]. 2, 82
31. D. Bak, Y. Hyakutake and N. Ohta, "Phase moduli space of supertubes," Nucl. Phys. B 696, 251 (2004) [arXiv:hep-th/0404104]. 2, 82
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]. 2, 82
33. D. Mateos and P. K. Townsend, "Supertubes," Phys. Rev. Lett. 87, 011602 (2001) [arXiv:hepth/0103030]. 3, 7, 9, 10, 41
34. D. Mateos, S. Ng and P. K. Townsend, "Supercurves," Phys. Lett. B 538, 366 (2002) [arXiv:hep-th/0204062]. 3, 10
35. R. Emparan, D. Mateos and P. K. Townsend, "Supergravity supertubes," JHEP 0107, 011 (2001) [arXiv:hep-th/0106012]. 3
36. O. Lunin and S. D. Mathur, "Metric of the multiply wound rotating string," Nucl. Phys. B 610, 49 (2001) [arXiv:hep-th/0105136]. 3
37. A. Sen, "Extremal black holes and elementary string states," Mod. Phys. Lett. A 10, 2081 (1995) [arXiv:hep-th/9504147]. 3
38. I. Bena and P. Kraus, "Three charge supertubes and black hole hair," Phys. Rev. D 70, 046003 (2004) [arXiv:hep-th/0402144]. 5, 8, 10, 14, 15
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]. 6, 77
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]. 6, 77
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]. 6
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]. 6, 48, 60, 82
43. S. Giusto and S. D. Mathur, "Geometry of D1-D5-P bound states," Nucl. Phys. B 729, 203 (2005) [arXiv:hep-th/0409067]. 6, 48, 60
44. S. Giusto, S. D. Mathur and Y. K. Srivastava, "A microstate for the 3-charge black ring," arXiv:hep-th/0601193. 6, 48
45. O. Lunin, "Adding momentum to D1-D5 system," JHEP 0404, 054 (2004) [arXiv:hepth/0404006]. 6, 48
46. I. Bena and P. Kraus, "Microstates of the D1-D5-KK system," Phys. Rev. D 72, 025007 (2005) [arXiv:hep-th/0503053]. 6, 18, 33, 41, 44, 49, 79
47. I. Bena and N. P. Warner, "Bubbling supertubes and foaming black holes," Phys. Rev. D 74, 066001 (2006) [arXiv:hep-th/0505166]. 6, 49
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]. 6, 35, 49, 53
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]. 6, 49
50. S. Giusto, S. D. Mathur and Y. K. Srivastava, "A microstate for the 3-charge black ring," arXiv:hep-th/0601193. 6
51. I. Bena, C. W. Wang and N. P. Warner, "The foaming three-charge black hole," arXiv:hepth/0604110. 6, 59, 62
52. V. Balasubramanian, E. G. Gimon and T. S. Levi, "Four dimensional black hole microstates: From D-branes to spaceEime foam," arXiv:hep-th/0606118. 6
53. I. Bena, C. W. Wang and N. P. Warner, "Mergers and typical black hole microstates," JHEP 0611, 042 (2006) [arXiv:hep-th/0608217]. 6, 63, 64, 73, 75
54. M. C. N. Cheng, "More bubbling solutions," arXiv:hep-th/0611156. 6
55. J. Ford, S. Giusto and A. Saxena, "A class of BPS time-dependent 3-charge microstates from spectral flow," arXiv:hep-th/0612227. 6
56. I. Bena and P. Kraus, "Microscopic description of black rings in AdS/CFT," JHEP 0412, 070 (2004) [arXiv:hep-th/0408186]. 6, 23, 40, 41, 43, 77, 78
57. A. Dabholkar, "Exact counting of black hole microstates," Phys. Rev. Lett. 94, 241301 (2005) [arXiv:hep-th/0409148]. 6
58. S. Ferrara and R. Kallosh, "Supersymmetry and attractors," Phys. Rev. D 54, 1514 (1996) [arXiv:hep-th/9602136]. 6
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]. 6
60. P. Kraus, "Lectures on black holes and the AdS(3)/CFT(2) correspondence," arXiv:hepth/0609074. 6
61. B. Pioline, "Lectures on on black holes, topological strings and quantum attractors," Class. Quant. Grav. 23, S981 (2006) [arXiv:hep-th/0607227]. 6
62. A. Sen, "How does a fundamental string stretch its horizon?," JHEP 0505, 059 (2005) [arXiv:hep-th/0411255]. 6
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]. 6
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]. 6
65. A. Dabholkar, N. Iizuka, A. Iqubal, A. Sen and M. Shigemori, "Spinning strings as small black rings," arXiv:hep-th/0611166. 6
66. A. Dabholkar, A. Sen and S. Trivedi, "Black hole microstates and attractor without supersymmetry," arXiv:hep-th/0611143. 6
67. J. Polchinski and M. J. Strassler, "The string dual of a confining four-dimensional gauge theory," arXiv:hep-th/0003136. 8, 79, 84
68. I. Bena and N. P.Warner, "One ring to rule them all ... and in the darkness bind them?," Adv. Theor. Math. Phys. 9 (2005) 667-701 [arXiv:hep-th/0408106.] 11, 16, 17, 20, 38, 43, 65
69. I. Bena, C. W. Wang and N. P. Warner, "Black rings with varying charge density," JHEP 0603, 015 (2006) [arXiv:hep-th/0411072]. 11
70. W. I. Taylor, "Adhering 0-branes to 6-branes and 8-branes," Nucl. Phys. B 508, 122 (1997) [arXiv:hep-th/9705116]. 11
71. I. Bena, "Splitting hairs of the three charge black hole," Phys. Rev. D 70, 105018 (2004) [arXiv:hep-th/0404073]. 12, 16, 40
72. J. D. Jackson, Classical Electrodynamics, Wiley, New York, NY, 1975. 13
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]. 13, 14, 78
74. C. A. R. Herdeiro, "Special properties of five dimensional BPS rotating black holes," Nucl. Phys. B 582, 363 (2000) [arXiv:hep-th/0003063]. 14
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]. 15
76. H. S. Reall, "Higher dimensional black holes and supersymmetry," Phys. Rev. D 68, 024024 (2003) [arXiv:hep-th/0211290]. 16
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]. 16, 21
78. H. Elvang, R. Emparan, D. Mateos and H. S. Reall, "Supersymmetric black rings and threecharge supertubes," Phys. Rev. D 71, 024033 (2005) [arXiv:hep-th/0408120]. 16, 43
79. J. P. Gauntlett and J. B. Gutowski, "General concentric black rings," Phys. Rev. D 71, 045002 (2005) [arXiv:hep-th/0408122]. 16, 31, 39, 44, 65
80. S. W. Hawking, "Gravitational Instantons," Phys. Lett. A 60, 81 (1977). 18, 26
81. D. Gaiotto, A. Strominger and X. Yin, "New connections between 4D and 5D black holes," JHEP 0602, 024 (2006) [arXiv:hep-th/0503217]. 18, 41
82. D. Gaiotto, A. Strominger and X. Yin, "5D black rings and 4D black holes," JHEP 0602, 023 (2006) [arXiv:hep-th/0504126]. 18, 33, 39, 43, 44, 49
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]. 18, 33, 39, 44, 49
84. I. Bena, P. Kraus and N. P. Warner, "Black rings in Taub-NUT," Phys. Rev. D 72, 084019 (2005) [arXiv:hep-th/0504142]. 18, 33, 37, 39, 43, 44, 49
85. I. R. Klebanov and A. A. Tseytlin, "Gravity duals of supersymmetric SU(N) × SU(N+M) gauge theories," Nucl. Phys. B 578, 123 (2000) [arXiv:hep-th/0002159]. 19
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:hepth/0007191]. 19, 45
87. A. W. Peet, "TASI lectures on black holes in string theory," arXiv:hep-th/0008241. 20, 22
88. R. Emparan and H. S. Reall, "Black rings," Class. Quant. Grav. 23 R169 (2006) [arXiv:hepth/0608012]. 21
89. H. Elvang and P. Figueras, "Black Saturn," arXiv:hep-th/0701035. 21
90. R. Emparan and H. S. Reall, "A rotating black ring in five dimensions," Phys. Rev. Lett. 88, 101101 (2002) [arXiv:hep-th/0110260]. 21
91. R. Emparan, "Rotating circular strings, and infinite non-uniqueness of black rings," JHEP 0403, 064 (2004) [arXiv:hep-th/0402149]. 21
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]. 21
93. I. Bena, C. W. Wang and N. P. Warner, "Sliding rings and spinning holes," JHEP 0605, 075 (2006) [arXiv:hep-th/0512157]. 24, 44, 63, 65, 67
94. G. W. Gibbons and S. W. Hawking, "Gravitational Multi - Instantons," Phys. Lett. B 78, 430 (1978). 26
95. G. W. Gibbons and P. J. Ruback, "The Hidden Symmetries of Multi-Center Metrics," Commun. Math. Phys. 115, 267 (1988). 27, 47
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]. 31
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]. 33, 41
98. F. Denef, "Supergravity flows and D-brane stability," JHEP 0008, 050 (2000) [arXiv:hepth/0005049]. 33, 41, 44, 52
99. B. Bates and F. Denef, "Exact solutions for supersymmetric stationary black hole composites," arXiv:hep-th/0304094. 33, 41, 44, 52
100. F. Denef, "Quantum quivers and Hall/hole halos," JHEP 0210, 023 (2002) [arXiv:hepth/0206072]. 33, 41, 44, 52
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]. 34
102. S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time, Cambridge University Press, Cambridge, 1975. 35
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]. 36, 82, 84
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]. 36
105. J. P. Gauntlett and J. B. Gutowski, "Concentric black rings," Phys. Rev. D 71, 025013 (2005) [arXiv:hep-th/0408010]. 39, 44
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]. 43, 44
107. J. M. Maldacena, A. Strominger and E. Witten, "Black hole entropy in M-theory," JHEP 9712, 002 (1997) [arXiv:hep-th/9711053]. 43
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]. 43
109. R. Dijkgraaf, J. M. Maldacena, G. W. Moore and E. P. Verlinde, "A black hole farey tail," arXiv:hep-th/0005003. 43
110. P. Kraus and F. Larsen, "Partition functions and elliptic genera from supergravity," arXiv:hepth/0607138. 43
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]. 43
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]. 43
113. M. Guica, L. Huang, W. Li and A. Strominger, JHEP 0610, 036 (2006) [arXiv:hepth/0505188]. 44
114. I. Bena and P. Kraus, "R**2 corrections to black ring entropy," arXiv:hep-th/0506015. 44
115. R. Gopakumar and C. Vafa, "On the gauge theory/geometry correspondence," Adv. Theor. Math. Phys. 3, 1415 (1999) [arXiv:hep-th/9811131]. 45
116. C. Vafa, "Superstrings and topological strings at large N," J. Math. Phys. 42, 2798 (2001) [arXiv:hep-th/0008142]. 45
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]. 45, 79, 85
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]. 45
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]. 48
120. J. M. Maldacena and L. Susskind, "D-branes and fat black holes," Nucl. Phys. B 475, 679 (1996) [arXiv:hep-th/9604042]. 77
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]. 79, 84
122. M. T. Grisaru, R. C. Myers and O. Tafjord, "SUSY and Goliath," JHEP 0008(2000) 040 [arXiv:hep-th/0008015]. 79, 84
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]. 79, 84
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]. 79, 84
125. I. Bena and C. Ciocarlie, "Exact N = 2 supergravity solutions with polarized branes," Phys. Rev. D 70, 086005 (2004) [arXiv:hep-th/0212252]. 79
126. I. Bena and R. Roiban, "N = 1* in 5 dimensions: Dijkgraaf-Vafa meets Polchinski-Strassler," JHEP 0311, 001 (2003) [arXiv:hep-th/0308013]. 79
127. Y. K. Srivastava, "Perturbations of supertube in KK monopole background," arXiv:hepth/0611320. 79
128. A. Saxena, General 3-charge geometries in 4 dimensions (to appear) 79
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]. 82
130. J. M. Maldacena and L. Susskind, "D-branes and fat black holes," Nucl. Phys. B 475, 679 (1996) [arXiv:hep-th/9604042]. 82
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]. 83
132. J. M. Maldacena, "Statistical entropy of near extremal five-branes," Nucl. Phys. B 477, 168 (1996) [arXiv:hep-th/9605016]. 83
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]. 83
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]. 83
135. B. D. Chowdhury and S. D. Mathur, "Fractional brane state in the early universe," arXiv:hepth/0611330. 83
136. R. Gregory and R. Laflamme, "Black strings and p-branes are unstable," Phys. Rev. Lett. 70, 2837 (1993) [arXiv:hep-th/9301052]. 83
137. T. Harmark, V. Niarchos and N. A. Obers, "Instabilities of black strings and branes," (Review) arXiv:hep-th/0701022. 83
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. 83
139. T. Harmark, K. R. Kristjansson, N. A. Obers and P. B. Ronne, "Three-charge black holes on a circle," arXiv:hep-th/0606246. 83
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]. 84
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]. 84
142. V. Balasubramanian, B. Czech, V. Hubeny, K. Larjo, M. Rangamani and J. Simon, "Typicality versus thermality: An analytic distinction," arXiv:hep-th/0701122. 86
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]. 86
144. J. M. Maldacena, "Eternal black holes in Anti-de-Sitter," JHEP 0304 021 (2003) [arXiv:hepth/0106112]. 86
145. D. Astefanesei, K. Goldstein and S. Mahapatra, "Moduli and (un)attractor black hole thermodynamics," arXiv:hep-th/0611140. 6
146. A. Sen, "Black hole entropy function and the attractor mechanism in higher derivative gravity," JHEP 0509, 038 (2005) [arXiv:hep-th/0506177]. 6
147. P. Kraus and F. Larsen, "Holographic gravitational anomalies," JHEP 0601, 022 (2006) [arXiv:hep-th/0508218]. 6
148. P. Kraus and F. Larsen, "Microscopic black hole entropy in theories with higher derivatives," JHEP 0509, 034 (2005) [arXiv:hep-th/0506176]. 6
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]. 6
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]. 84