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On the phase structure and thermodynamic geometry of R-charged black holes

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Abstract

We study the phase structure and equilibrium state space geometry of R-charged black holes in D = 5, 4 and 7 and the corresponding rotating D3, M2 and M5 branes. For various charge configurations of the compact black holes in the canonical ensemble we demonstrate new liquid-gas like phase coexistence behaviour culminating in second order critical points. The critical exponents turn out to be the same as that of four dimensional asymptotically AdS black holes in Einstein Maxwell theory. We further establish that the regions of stability for R-charged black holes are, in some cases, more constrained than is currently believed, due to properties of some of the response coefficients. The equilibrium state space scalar curvature is calculated for various charge configurations, both for the case of compact as well as flat horizons and its asymptotic behaviour with temperature is established.

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References

  1. R.M. Wald, The thermodynamics of black holes, Living Rev. Rel. 4 (2001) 6 [gr-qc/9912119] [SPIRES].

    Google Scholar 

  2. D.N. Page, Hawking radiation and black hole thermodynamics, New J. Phys. 7 (2005) 203 [hep-th/0409024] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  3. 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 

  4. E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. T heor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [SPIRES].

    MATH  MathSciNet  Google Scholar 

  5. S.S. Gubser, Thermodynamics of spinning D3-branes, Nucl. Phys. B 551 (1999) 667 [hep-th/9810225] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  6. R.-G. Cai and K.-S. Soh, Critical behavior in the rotating D-branes, Mod. Phys. Lett. A 14 (1999) 1895 [hep-th/9812121] [SPIRES].

    ADS  Google Scholar 

  7. M. Cvetič and S.S. Gubser, Phases of R-charged black holes, spinning branes and strongly coupled gauge theories, JHEP 04 (1999) 024 [hep-th/9902195] [SPIRES].

    Article  ADS  Google Scholar 

  8. M. Cvetič and S.S. Gubser, Thermodynamic Stability and Phases of General Spinning Branes, JHEP 07 (1999) 010 [hep-th/9903132] [SPIRES].

    Article  ADS  Google Scholar 

  9. A. Chamblin, R. Emparan, C.V. Johnson and R.C. Myers, Charged AdS black holes and catastrophic holography, Phys. Rev. D 60 (1999) 064018 [hep-th/9902170] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  10. A. Chamblin, R. Emparan, C.V. Johnson and R.C. Myers, Holography, thermodynamics and fluctuations of charged AdS black holes, Phys. Rev. D 60 (1999) 104026 [hep-th/9904197] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  11. A. Sahay, T. Sarkar and G. Sengupta, Thermodynamic Geometry and Phase Transitions in Kerr-Newman-AdS Black Holes, JHEP 04 (2010) 118 [arXiv:1002.2538] [SPIRES].

    Article  ADS  Google Scholar 

  12. A. Sahay, T. Sarkar and G. Sengupta, On the Thermodynamic Geometry and Critical Phenomena of AdS Black Holes, JHEP 07 (2010) 082 [arXiv:1004.1625] [SPIRES].

    Article  ADS  Google Scholar 

  13. R. Banerjee, S. Ghosh and D. Roychowdhury, New type of phase transition in Reissner Nordstrom-AdS black hole and its thermodynamic geometry, arXiv:1008.2644 [SPIRES].

  14. K. Behrndt, M. Cvetič and W.A. Sabra, Non-extreme black holes of five dimensional N = 2 AdS supergravity, Nucl. Phys. B 553 (1999) 317 [hep-th/9810227] [SPIRES].

    Article  ADS  Google Scholar 

  15. L. Tisza, Generalized Thermodynamics, MIT Press, Cambridge, MA, U.S.A. (1966).

    Google Scholar 

  16. H.B. Callen, Thermodynamics and an Introcution to Thermostatitics, Wiley, New York, U.S.A. (1985).

    Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  18. 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 

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

    ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  21. 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 

  22. 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 

  23. H.E. Stanley, Scaling, universality, and renormalization: Three pillars of modern critical phenomena, Rev. Mod. Phys. 71 (1999) S358.

    Article  Google Scholar 

  24. M. E. Fisher, Scaling, Universality and Renormalization Group Theory, Lecture Notes in Physics, 186 (1983), F.J.W. Hahne ed., Springer, Berlin, p. 1-139.

    Google Scholar 

  25. 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 

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

    Article  MathSciNet  ADS  Google Scholar 

  27. X.N. Wu, Multicritical phenomena of Reissner-Nordstrom anti-de Sitter black holes, Phys. Rev. D 62 (2000) 124023 [SPIRES].

    ADS  Google Scholar 

  28. D. Yamada and L.G. Yaffe, Phase diagram of N = 4 super-Yang-Mills theory with R-symmetry chemical potentials, JHEP 09 (2006) 027 [hep-th/0602074] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  29. S. Jain, S. Mukherji and S. Mukhopadhyay, Notes on R-charged black holes near criticality and gauge theory, JHEP 11 (2009) 051 [arXiv:0906.5134] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Indian Institute of Technology, Kanpur, 208016, India

    Anurag Sahay, Tapobrata Sarkar & Gautam Sengupta

Authors
  1. Anurag Sahay
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  2. Tapobrata Sarkar
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  3. Gautam Sengupta
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Correspondence to Tapobrata Sarkar.

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Sahay, A., Sarkar, T. & Sengupta, G. On the phase structure and thermodynamic geometry of R-charged black holes. J. High Energ. Phys. 2010, 125 (2010). https://doi.org/10.1007/JHEP11(2010)125

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  • DOI: https://doi.org/10.1007/JHEP11(2010)125

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