Skip to main content
SpringerLink
Log in

An exact fluctuating 1/2-BPS configuration

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

This work explores the role of thermodynamic fluctuations in the two parameter giant and superstar configurations characterized by an ensemble of arbitrary liquid droplets or irregular shaped fuzzballs. Our analysis illustrates that the chemical and state-space geometric descriptions exhibit an intriguing set of exact pair correction functions and the global correlation lengths. The first principle of statistical mechanics shows that the possible canonical fluctuations may precisely be ascertained without any approximation. Interestingly, our intrinsic geometric study exemplifies that there exist exact fluctuating 1/2-BPS statistical configurations which involve an ensemble of microstates describing the liquid droplets or fuzzballs. The Gaussian fluctuations over an equilibrium chemical and state-space configurations accomplish a well-defined, non-degenerate, curved and regular intrinsic Riemannian manifolds for all physically admissible domains of black hole parameters. An explicit computation demonstrates that the underlying chemical correlations involve ordinary summations, whilst the state-space correlations may simply be depicted by standard polygamma functions. Our construction ascribes definite stability character to the canonical energy fluctuations and to the counting entropy associated with an arbitrary choice of excited boxes from an ensemble of ample boxes constituting a variety of Young tableaux.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. 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 

  2. V. Balasubramanian, M. Berkooz, A. Naqvi and M.J. Strassler, Giant gravitons in conformal field theory, JHEP 04 (2002) 034 [hep-th/0107119] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  3. V. Balasubramanian, J. de Boer, V. Jejjala and J. Simon, Entropy of near-extremal black holes in AdS 5, JHEP 05 (2008) 067 [arXiv:0707.3601] [SPIRES].

    Article  ADS  Google Scholar 

  4. K. Huang, Statistical Mechanics, John Wiley, New York U.S.A. (1963).

    Google Scholar 

  5. L.D. Landau, E.M. Lifshitz, Statistical Physics-I, II, Pergamon, Oxford U.K. (1969).

    Google Scholar 

  6. 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 

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

    MathSciNet  ADS  Google Scholar 

  8. 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 

  9. 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 

  10. S.S. Gubser and J.J. Heckman, Thermodynamics of R-charged black holes in AdS 5 from effective strings, JHEP 11 (2004) 052 [hep-th/0411001] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  11. S.D. Mathur, Where are the states of a black hole?, [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. J. Simon, Small Black holes vs horizonless solutions in AdS, Phys. Rev. D 81 (2010) 024003 [arXiv:0910.3225] [SPIRES].

    ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  15. F. Weinhold, Metric geometry of equilibrium thermodynamics. Scaling, homogeneity, and generalized GibbsDuhem relations, J. Chem. Phys 63 (1975) 2484.

    Article  MathSciNet  ADS  Google Scholar 

  16. G. Ruppeiner, Riemannian geometry in thermodynamic fluctuation theory, Rev. Mod. Phys. 67 (1995) 605 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  17. M. Santoro, A.S. Benight, On the geometrical thermodynamics of chemical reactions, math-ph/0507026.

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

    ADS  Google Scholar 

  19. G. Ruppeiner, Thermodynamic Critical Fluctuation Theory?, Phys. Rev. Lett. 50 (1983) 287 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

  23. 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 

  24. 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 

  25. S. Bellucci, S. Ferrara and A. Marrani, Attractor horizon geometries of extremal black holes, hep-th/0702019 [SPIRES].

  26. S. Bellucci, S. Ferrara and A. Marrani, Attractors in Black, Fortsch. Phys. 56 (2008) 761 [arXiv:0805.1310] [SPIRES].

    Article  MathSciNet  Google Scholar 

  27. G. Ruppeiner, Stability and fluctuations in black hole thermodynamics, Phys. Rev. D 75 (2007) 024037 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  28. S. Ferrara, G.W. Gibbons and R. Kallosh, Black holes and critical points in moduli space, Nucl. Phys. B 500 (1997) 75 [hep-th/9702103] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  29. 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 

  30. 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 

  31. 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 

  32. 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 

  33. 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 

  34. G. Ruppeiner, Thermodynamic curvature and phase transitions in Kerr-Newman black holes, Phy. Rev. D 78 (2008) 024016.

    MathSciNet  ADS  Google Scholar 

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

    Article  Google Scholar 

  36. S. Bellucci and B.N. Tiwari, On the Microscopic Perspective of Black Branes Thermodynamic Geometry, arXiv:0808.3921 [SPIRES].

  37. S. Bellucci, B.N. Tiwari, State-space Manifold and Rotating Black Holes, to appear.

  38. S. Bellucci, B.N. Tiwari, Black Strings, Black Rings and State-space Manifold, to appear.

  39. 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 

  40. 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 

  41. S. Corley, A. Jevicki and S. Ramgoolam, Exact correlators of giant gravitons from dual N = 4 SYM theory, Adv. Theor. Math. Phys. 5 (2002) 809 [hep-th/0111222] [SPIRES].

    MathSciNet  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  44. 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 

  45. S.W. Hawking and D.N. Page, Thermodynamics of Black Holes in anti-de Sitter Space, Commun. Math. Phys. 87 (1983) 577 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  46. E.G. Gimon, F. Larsen and J. Simon, Black Holes in Supergravity: the non-BPS Branch, JHEP 01 (2008) 040 [arXiv:0710.4967] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

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

    MATH  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Stefano Bellucci & Bhupendra Nath Tiwari

  2. Department of Physics, Indian Institute of Technology Kanpur, Kanpur, -208016, Uttar Pradesh, India

    Bhupendra Nath Tiwari

Authors
  1. Stefano Bellucci
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bhupendra Nath Tiwari
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stefano Bellucci.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bellucci, S., Nath Tiwari, B. An exact fluctuating 1/2-BPS configuration. J. High Energ. Phys. 2010, 23 (2010). https://doi.org/10.1007/JHEP05(2010)023

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP05(2010)023

Keywords

Search

Navigation