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State-space manifold and rotating black holes

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Abstract

We study a class of fluctuating higher dimensional black hole configurations obtained in string theory/M-theory compactifications. We explore the intrinsic Riemannian geometric nature of Gaussian fluctuations arising from the Hessian of the coarse graining entropy, defined over an ensemble of brane microstates. It has been shown that the state-space geometry spanned by the set of invariant parameters is non-degenerate, regular and has a negative scalar curvature for the rotating Myers-Perry black holes, Kaluza-Klein black holes, supersymmetric AdS 5 black holes, D 1-D 5 configurations and the associated BMPV black holes. Interestingly, these solutions demonstrate that the principal components of the state-space metric tensor admit a positive definite form, while the off diagonal components do not. Furthermore, the ratio of diagonal components weakens relatively faster than the off diagonal components, and thus they swiftly come into an equilibrium statistical configuration. Novel aspects of the scaling property suggest that the brane-brane statistical pair correlation functions divulge an asymmetric nature, in comparison with the others. This approach indicates that all above configurations are effectively attractive and stable, on an arbitrary hyper-surface of the state-space manifolds. It is nevertheless noticed that there exists an intriguing relationship between non-ideal inter-brane statistical interactions and phase transitions. The ramifications thus described are consistent with the existing picture of the microscopic CFTs. We conclude 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. A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  2. C.G. Callan and J.M. Maldacena, D-brane approach to black hole quantum mechanics, Nucl. Phys. B 472 (1996) 591 [hep-th/9602043] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  3. S.D. Mathur, Black hole size and phase space volumes, arXiv:0706.3884 [SPIRES].

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

    Article  MATH  MathSciNet  Google Scholar 

  5. J.M. Maldacena, Gravity, particle physics and their unification, hep-ph/0002092 [SPIRES].

  6. S. Bellucci, E. Ivanov and S. Krivonos, AdS/CFT equivalence transformation, Phys. Rev. D 66 (2002) 086001 [Erratum ibid. D 67 (2003) 049901] [hep-th/0206126] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  7. S. Bellucci, A. Galajinsky, E. Ivanov and S. Krivonos, AdS 2 /CFT 1 , canonical transformations and superconformal mechanics, Phys. Lett. B 555 (2003) 99 [hep-th/0212204] [SPIRES].

    ADS  Google Scholar 

  8. S.W. Hawking, Black holes in general relativity, Commun. Math. Phys. 25 (1972) 152 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  9. D.C. Robinson, Uniqueness of the Kerr black hole, Phys. Rev. Lett. 34 (1975) 905 [SPIRES].

    Article  ADS  Google Scholar 

  10. P.O. Mazur, Proof of uniqueness of the Kerr-Newman black hole solution, J. Phys. A 15 (1982) 3173 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  11. S.D. Mathur, Where are the states of a black hole?, OHSTPY-HEP-T-04-001 [hep-th/0401115] [SPIRES].

  12. S.D. Mathur, A. Saxena and Y.K. Srivastava, Constructing ‘hair’ for the three charge hole, Nucl. Phys. B 680 (2004) 415 [hep-th/0311092] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  14. R.C. Myers and M.J. Perry, Black holes in higher dimensional space-times, Ann. Phys. 172 (1986) 304 [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  15. G.W. Gibbons and D.L. Wiltshire, Black holes in Kaluza-Klein theory, Ann. Phys. 167 (1986) 201 [Erratum ibid. 176 (1987) 393] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  16. N. Itzhaki, D6 + D0and five-dimensional spinning black hole, JHEP 09 (1998) 018 [hep-th/9809063] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  17. V. Balasubramanian and F. Larsen, On D-branes and black holes in four dimensions, Nucl. Phys. B 478 (1996) 199 [hep-th/9604189] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  18. B.N. Tiwari, Sur les corrections de la géométrie thermodynamique des trous noirs, arXiv:0801.4087 [SPIRES].

  19. H. Lin, O. Lunin and J.M. Maldacena, Bubbling AdS space and 1/2 BPS geometries, JHEP 10 (2004) 025 [hep-th/0409174] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  20. D. Berenstein, A toy model for the AdS/CFT correspondence, JHEP 07 (2004) 018 [hep-th/0403110] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  21. N.V. Suryanarayana, Half-BPS giants, free fermions and microstates of superstars, JHEP 01 (2006) 082 [hep-th/0411145] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  22. M.M. Sheikh-Jabbari and M. Torabian, Classification of all 1/2 BPS solutions of the tiny graviton matrix theory, JHEP 04 (2005) 001 [hep-th/0501001] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  23. G. Mandal, Fermions from half-BPS supergravity, JHEP 08 (2005) 052 [hep-th/0502104] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  24. L. Grant, L. Maoz, J. Marsano, K. Papadodimas and V.S. Rychkov, Minisuperspace quantization of ‘bubbling AdS’ and free fermion droplets, JHEP 08 (2005) 025 [hep-th/0505079] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  25. A. Dhar, G. Mandal and M. Smedback, From gravitons to giants, JHEP 03 (2006) 031 [hep-th/0512312] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  26. J.B. Gutowski and H.S. Reall, Supersymmetric AdS 5 black holes, JHEP 02 (2004) 006 [hep-th/0401042] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  27. J.B. Gutowski and H.S. Reall, General supersymmetric AdS 5 black holes, JHEP 04 (2004) 048 [hep-th/0401129] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  28. Z.W. Chong, M. Cvetič, H. Lü and C.N. Pope, Five-dimensional gauged supergravity black holes with independent rotation parameters, Phys. Rev. D 72 (2005) 041901 [hep-th/0505112] [SPIRES].

    ADS  Google Scholar 

  29. Z.W. Chong, M. Cvetič, H. Lü and C.N. Pope, General non-extremal rotating black holes in minimal five-dimensional gauged supergravity, Phys. Rev. Lett. 95 (2005) 161301 [hep-th/0506029] [SPIRES].

    Article  ADS  Google Scholar 

  30. H.K. Kunduri, J. Lucietti and H.S. Reall, Supersymmetric multi-charge AdS 5 black holes, JHEP 04 (2006) 036 [hep-th/0601156] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  31. R.C. Myers and O. Tafjord, Superstars and giant gravitons, JHEP 11 (2001) 009 [hep-th/0109127] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  32. K. Behrndt, A.H. Chamseddine and W.A. Sabra, BPS black holes in N = 2 five dimensional AdS supergravity, Phys. Lett. B 442 (1998) 97 [hep-th/9807187] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  33. J. Kinney, J.M. Maldacena, S. Minwalla and S. Raju, An index for 4 dimensional super conformal theories, Commun. Math. Phys. 275 (2007) 209 [hep-th/0510251] [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  34. M. Berkooz, D. Reichmann and J. Simon, A Fermi surface model for large supersymmetric AdS 5 black holes, JHEP 01 (2007) 048 [hep-th/0604023] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  35. S. Kim and K.-M. Lee, 1/16-BPS black holes and giant gravitons in the AdS 5 × S 5 space, JHEP 12 (2006) 077 [hep-th/0607085] [SPIRES].

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  37. S.D. Mathur, The fuzzball proposal for black holes: an elementary review, Fortsch. Phys. 53 (2005) 793 [hep-th/0502050] [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  38. S. Bellucci and B.N. Tiwari, On the microscopic perspective of black branes thermodynamic geometry, Entropy 12 (2010) 2097 [arXiv:0808.3921] [SPIRES].

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  40. J.C. Breckenridge et al., Macroscopic and microscopic entropy of near-extremal spinning black holes, Phys. Lett. B 381 (1996) 423 [hep-th/9603078] [SPIRES].

    MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  42. H. Elvang, A charged rotating black ring, Phys. Rev. D 68 (2003) 124016 [hep-th/0305247] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  43. H. Elvang and R. Emparan, Black rings, supertubes and a stringy resolution of black hole non-uniqueness, JHEP 11 (2003) 035 [hep-th/0310008] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  44. S. Ferrara, R. Kallosh and A. Strominger, N = 2 extremal black holes, Phys. Rev. D 52 (1995) 5412 [hep-th/9508072] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  45. A. Strominger, Macroscopic entropy of N = 2 extremal black holes, Phys. Lett. B 383 (1996) 39 [hep-th/9602111] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  46. J.M. Maldacena, Black holes in string theory, Ph.D. Thesis, Princeton University (1996) [hep-th/9607235] [SPIRES].

  47. J.M. Maldacena, A. Strominger and E. Witten, Black hole entropy in M-theory, JHEP 12 (1997) 002 [hep-th/9711053] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

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

    MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  50. G. Moore, Introduction to modular functions and their application to 2D CFT, Spring School on Superstring Theory and Related Topics, ICTP Trieste, Italy (2008) http://cdsagenda5.ictp.trieste.it.

  51. M.R. Gaberdiel, S. Gukov, C.A. Keller, G.W. Moore and H. Ooguri, Extremal N = (2, 2) 2D conformal field theories and constraints of modularity, arXiv:0805.4216 [SPIRES].

  52. A. Sen, Entropy function and AdS 2 /CFT 1 correspondence, JHEP 11 (2008) 075 [arXiv:0805.0095] [SPIRES].

    Article  ADS  Google Scholar 

  53. R.K. Gupta and A. Sen, AdS 3 /CFT 2 to AdS 2 /CFT 1, JHEP 04 (2009) 034 [arXiv:0806.0053] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  54. D. Gaiotto and X. Yin, Genus two partition functions of extremal conformal field theories, JHEP 08 (2007) 029 [arXiv:0707.3437] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  55. A. Belhaj, On black objects in type IIA superstring theory on Calabi-Yau manifolds, AJMP 6 (2008) 49 [arXiv:0809.1114] [SPIRES].

    MATH  Google Scholar 

  56. G. Lopes Cardoso, B. de Wit, J. Kappeli and T. Mohaupt, Asymptotic degeneracy of dyonic N = 4 string states and black hole entropy, JHEP 12 (2004) 075 [hep-th/0412287] [SPIRES].

    ADS  Google Scholar 

  57. A. Sen, Black holes and the spectrum of half-BPS states in N = 4 supersymmetric string theory, Adv. Theor. Math. Phys. 9 (2005) 527 [hep-th/0504005] [SPIRES].

    MATH  MathSciNet  Google Scholar 

  58. F. Weinhold, Metric geometry of equilibrium thermodynamics, J. Chem. Phys. 63 (1975) 2479.

    Article  MathSciNet  ADS  Google Scholar 

  59. F. Weinhold, Metric geometry of equilibrium thermodynamics. II. Scaling, homogeneity, and generalized Gibbs-Duhem relations, J. Chem. Phys. 63 (1975) 2484.

    Article  MathSciNet  ADS  Google Scholar 

  60. G. Ruppeiner, Riemannian geometry in thermodynamic fluctuation theory, Rev. Mod. Phys. 67 (1995) 605 [Erratum ibid. 68 (1996) 313] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  61. G. Ruppeiner, Thermodynamics: a Riemannian geometric model, Phys. Rev. A 20 (1979) 1608.

    ADS  Google Scholar 

  62. G. Ruppeiner, Thermodynamic critical fluctuation theory?, Phys. Rev. Lett. 50 (1983) 287 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  63. G. Ruppeiner, New thermodynamic fluctuation theory using path integrals, Phys. Rev. A 27 (1983) 1116.

    ADS  Google Scholar 

  64. G. Ruppeiner and C. Davis, Thermodynamic curvature of the multicomponent ideal gas, Phys. Rev. A 41 (1990) 2200.

    ADS  Google Scholar 

  65. J.-y. Shen, R.-G. Cai, B. Wang and R.-K. Su, Thermodynamic geometry and critical behavior of black holes, Int. J. Mod. Phys. A 22 (2007) 11 [gr-qc/0512035] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  66. J.E. Aman, I. Bengtsson and N. Pidokrajt, Flat information geometries in black hole thermodynamics, Gen. Rel. Grav. 38 (2006) 1305 [gr-qc/0601119] [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  67. J.E. Aman, I. Bengtsson and N. Pidokrajt, Geometry of black hole thermodynamics, Gen. Rel. Grav. 35 (2003) 1733 [gr-qc/0304015] [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  68. J.E. Aman and N. Pidokrajt, Geometry of higher-dimensional black hole thermodynamics, Phys. Rev. D 73 (2006) 024017 [hep-th/0510139] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  69. T. Sarkar, G. Sengupta and B. Nath Tiwari, On the thermodynamic geometry of BTZ black holes, JHEP 11 (2006) 015 [hep-th/0606084] [SPIRES].

    Article  ADS  Google Scholar 

  70. V. Balasubramanian, J. de Boer, V. Jejjala and J. Simon, The library of Babel: on the origin of gravitational thermodynamics, JHEP 12 (2005) 006 [hep-th/0508023] [SPIRES].

    ADS  Google Scholar 

  71. T. Sarkar, G. Sengupta and B.N. Tiwari, Thermodynamic geometry and extremal black holes in string theory, JHEP 10 (2008) 076 [arXiv:0806.3513] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  72. S. Bellucci, V. Chandra and B.N. Tiwari, On the thermodynamic geometry of hot QCD, arXiv:0812.3792 [SPIRES].

  73. S. Bellucci, V. Chandra and B.N. Tiwari, Thermodynamic geometric stability of Quarkonia states, arXiv:1010.4225 [SPIRES].

  74. S. Bellucci, V. Chandra and B.N. Tiwari, A geometric approach to correlations and quark number susceptibilities, arXiv:1010.4405 [SPIRES].

  75. S. Bellucci and B.N. Tiwari, Thermodynamic geometry: evolution, correlation and phase transition, arXiv:1010.5148 [SPIRES].

  76. L.D. Landau and E.M. Lifshitz, Statistical Mechanics, Pergaman Press, Hungary (1980).

    Google Scholar 

  77. D. Tranah and P.T. Landsberg, Thermodynamics of non-extensive entropies II, Collect. Phenom. 3 (1980) 81.

    MathSciNet  Google Scholar 

  78. G. Arcioni and E. Lozano-Tellechea, Stability and critical phenomena of black holes and black rings, Phys. Rev. D 72 (2005) 104021 [hep-th/0412118] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  79. J.E. Aman and N. Pidokrajt, Geometry of higher-dimensional black hole thermodynamics, Phys. Rev. D 73 (2006) 024017 [hep-th/0510139] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  80. G. Ruppeiner, Thermodynamic curvature and phase transitions in Kerr-Newman black holes, Phys. Rev. D 78 (2008) 024016 [arXiv:0802.1326] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  81. J.D. Bekenstein, Information in the holographic universe, Sci. Am. 289 (2003) 58.

    Article  Google Scholar 

  82. W. Taylor, Adhering 0-branes to 6-branes and 8-branes, Nucl. Phys. B 508 (1997) 122 [hep-th/9705116] [SPIRES].

    Article  Google Scholar 

  83. R.R. Khuri and T. Ortín, A non-supersymmetric dyonic extreme Reissner-Nordstrom black hole, Phys. Lett. B 373 (1996) 56 [hep-th/9512178] [SPIRES].

    ADS  Google Scholar 

  84. G.T. Horowitz, J.M. Maldacena and A. Strominger, Nonextremal black hole microstates and U-duality, Phys. Lett. B 383 (1996) 151 [hep-th/9603109] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  85. U.H. Danielsson, A. Guijosa and M. Kruczenski, Brane-antibrane systems at finite temperature and the entropy of black branes, JHEP 09 (2001) 011 [hep-th/0106201] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  86. F. Larsen, Rotating Kaluza-Klein black holes, Nucl. Phys. B 575 (2000) 211 [hep-th/9909102] [SPIRES].

    Article  ADS  Google Scholar 

  87. D. Rasheed, The rotating dyonic black holes of Kaluza-Klein theory, Nucl. Phys. B 454 (1995) 379 [hep-th/9505038] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  88. F. Larsen, Kaluza-Klein black holes in string theory, hep-th/0002166 [SPIRES].

  89. J.M. Maldacena and A. Strominger, Statistical entropy of four-dimensional extremal black holes, Phys. Rev. Lett. 77 (1996) 428 [hep-th/9603060] [SPIRES].

    Article  ADS  Google Scholar 

  90. R. Gopakumar and M.B. Green, Instantons and non-renormalisation in AdS/CFT, JHEP 12 (1999) 015 [hep-th/9908020] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  91. J. Scherk, Antigravity: a crazy idea?, Phys. Lett. B 88 (1979) 265 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  92. J. Scherk, A survey of spin-5/2 theory, in Supergravity, P. van Nieuwenhuizen and D.Z. Freedman eds., North-Holland, Amsterdam (1979).

    Google Scholar 

  93. S. Bellucci and V. Faraoni, The equivalence principle, CP violations and the Higgs boson mass, Phys. Rev. D 49 (1994) 2922 [SPIRES].

    ADS  Google Scholar 

  94. S. Bellucci and V. Faraoni, Effects of the gravivector and graviscalar fields in N = 2, N = 8 supergravity, Phys. Lett. B 377 (1996) 55 [hep-ph/9605443] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  95. J.B. Gutowski and W. Sabra, General supersymmetric solutions of five-dimensional supergravity, JHEP 10 (2005) 039 [hep-th/0505185] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  96. M. Cvetič et al., Embedding AdS black holes in ten and eleven dimensions, Nucl. Phys. B 558 (1999) 96 [hep-th/9903214] [SPIRES].

    Article  ADS  Google Scholar 

  97. 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].

  98. 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].

    MathSciNet  ADS  Google Scholar 

  99. P.J. Silva, Thermodynamics at the BPS bound for black holes in AdS, JHEP 10 (2006) 022 [hep-th/0607056] [SPIRES].

    Article  ADS  Google Scholar 

  100. D. Mateos and P.K. Townsend, Supertubes, Phys. Rev. Lett. 87 (2001) 011602 [hep-th/0103030] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  101. B.C. Palmer and D. Marolf, Counting supertubes, JHEP 06 (2004) 028 [hep-th/0403025] [SPIRES].

    Article  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  104. A. Dabholkar, J.P. Gauntlett, J.A. Harvey and D. Waldram, Strings as solitons and black holes as strings, Nucl. Phys. B 474 (1996) 85 [hep-th/9511053] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  105. J.-H. Cho and P. Oh, Super D-helix, Phys. Rev. D 64 (2001) 106010 [hep-th/0105095] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  106. D. Mateos, S. Ng and P.K. Townsend, Supercurves, Phys. Lett. B 538 (2002) 366 [hep-th/0204062] [SPIRES].

    MathSciNet  ADS  Google Scholar 

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

    MathSciNet  ADS  Google Scholar 

  108. J.P. Gauntlett, R.C. Myers and P.K. Townsend, Black holes of D = 5 supergravity, Class. Quant. Grav. 16 (1999) 1 [hep-th/9810204] [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  109. A. Dabholkar, Microstates of non-supersymmetric black holes, Phys. Lett. B 402 (1997) 53 [hep-th/9702050] [SPIRES].

    MathSciNet  ADS  Google Scholar 

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

    MathSciNet  ADS  Google Scholar 

  111. R. Argurio, F. Englert and L. Houart, Statistical entropy of the four-dimensional Schwarzschild black hole, Phys. Lett. B 426 (1998) 275 [hep-th/9801053] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  112. H.J. Sheinblatt, Statistical entropy of an extremal black hole with 0- and 6-brane charge, Phys. Rev. D 57 (1998) 2421 [hep-th/9705054] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  113. A. Dhar and G. Mandal, Probing 4-dimensional nonsupersymmetric black holes carrying D0- and D6-brane charges, Nucl. Phys. B 531 (1998) 256 [hep-th/9803004] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  114. A. Mikhailov, Giant gravitons from holomorphic surfaces, JHEP 11 (2000) 027 [hep-th/0010206] [SPIRES].

    Article  ADS  Google Scholar 

  115. G. Mandal and N.V. Suryanarayana, Counting 1/8-BPS dual-giants, JHEP 03 (2007) 031 [hep-th/0606088] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  116. M. Awada and P.K. Townsend, N = 4 Maxwell-Einstein supergravity in five-dimensions and its SU(2) gauging, Nucl. Phys. B 255 (1985) 617 [SPIRES].

    Article  ADS  Google Scholar 

  117. 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] [SPIRES].

    ADS  Google Scholar 

  118. I. Bena and P. Kraus, Microscopic description of black rings in AdS/CFT, JHEP 12 (2004) 070 [hep-th/0408186] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

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

    MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  121. O. Lunin, J.M. Maldacena and L. Maoz, Gravity solutions for the D1-D5 system with angular momentum, hep-th/0212210 [SPIRES].

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

    MathSciNet  ADS  Google Scholar 

  123. S. Bellucci and B.N. Tiwari, State-space correlations and stabilities, Phys. Rev. D 82 (2010) 084008 [arXiv:0910.5309] [SPIRES].

    ADS  Google Scholar 

  124. S. Bellucci and B.N. Tiwari, An exact fluctuating 1/2-BPS configuration, JHEP 05 (2010) 023 [arXiv:0910.5314] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  125. S. Bellucci and B.N. Tiwari, Black strings, black rings and state-space manifold, arXiv:1010.3832 [SPIRES].

  126. S. Bellucci and B.N. Tiwari, Thermodynamic geometry and Hawking radiation, JHEP 11 (2010) 030 [arXiv:1009.0633] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  128. H. Elvang, R. Emparan, D. Mateos and H.S. Reall, Supersymmetric 4D rotating black holes from 5D black rings, JHEP 08 (2005) 042 [hep-th/0504125] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  129. R. Emparan, D. Mateos and P.K. Townsend, Supergravity supertubes, JHEP 07 (2001) 011 [hep-th/0106012] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  130. I. Bena, Splitting hairs of the three charge black hole, Phys. Rev. D 70 (2004) 105018 [hep-th/0404073] [SPIRES].

    MathSciNet  ADS  Google Scholar 

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  1. INFN-Laboratori Nazionali di Frascati, Via E. Fermi 40, 00044, Frascati, Italy

    Stefano Bellucci & Bhupendra Nath Tiwari

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  1. Stefano Bellucci
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  2. Bhupendra Nath Tiwari
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Correspondence to Stefano Bellucci.

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Bellucci, S., Tiwari, B.N. State-space manifold and rotating black holes. J. High Energ. Phys. 2011, 118 (2011). https://doi.org/10.1007/JHEP01(2011)118

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