Skip to main content
SpringerLink
Log in

Glassy phase transition and stability in black holes

  • Regular Article - Theoretical Physics
  • Published:
The European Physical Journal C Aims and scope Submit manuscript

Abstract

Black hole thermodynamics, confined to the semi-classical regime, cannot address the thermodynamic stability of a black hole in flat space. Here we show that inclusion of a correction beyond the semi-classical approximation makes a black hole thermodynamically stable. This stability is reached through a phase transition. By using Ehrenfest’s scheme we further prove that this is a glassy phase transition with a Prigogine–Defay ratio close to 3. This value is well within the desired bound (2 to 5) for a glassy phase transition. Thus our analysis indicates a very close connection between the phase transition phenomena of a black hole and glass forming systems. Finally, we discuss the robustness of our results by considering different normalisations for the correction term.

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. S.W. Hawking, Black holes and thermodynamics. Phys. Rev. D 13, 191 (1976)

    Article  MathSciNet  ADS  Google Scholar 

  2. P.C.W. Davies, Thermodynamics of black holes. Rep. Prog. Phys. 41, 1313 (1978)

    Article  ADS  Google Scholar 

  3. R. Banerjee, S.K. Modak, Exact differential and corrected area law for stationary black holes in tunneling method. J. High Energy Phys. 05, 063 (2009). arXiv:0903.3321

    Article  MathSciNet  ADS  Google Scholar 

  4. J.E. Lidsey, S. Nojiri, S.D. Odintsov, S. Ogushi, The AdS/CFT correspondence and logarithmic corrections to braneworld cosmology and the Cardy-Verlinde formula. Phys. Lett. B 544, 337 (2002). arXiv:hep-th/0207009

    Article  MATH  MathSciNet  ADS  Google Scholar 

  5. J. Jackle, Models of the glass transition. Rep. Prog. Phys. 49, 171 (1986)

    Article  ADS  Google Scholar 

  6. S.M. Carroll, An Introduction to General Relativity: Spacetime and Geometry (Addison Wesley, San Francisco, 2004)

    MATH  Google Scholar 

  7. R. Banerjee, B.R. Majhi, Quantum tunneling beyond semiclassical approximation. J. High Energy Phys. 0806, 095 (2008). arXiv:0805.2220 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  8. S.K. Modak, Corrected entropy of BTZ black hole in tunneling approach. Phys. Lett. B 671, 167 (2009). arXiv:0807.0959 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  9. R. Banerjee, B.R. Majhi, Quantum tunneling, trace anomaly and effective metric. Phys. Lett. B 674, 218 (2009). arXiv:0808.3688 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  10. B.R. Majhi, Fermion tunneling beyond semiclassical approximation. Phys. Rev. D 79, 044005 (2009). arXiv:0809.1508 [hep-th]

    Article  ADS  Google Scholar 

  11. B.R. Majhi, S. Samanta, Hawking radiation due to photon and gravitino tunneling. arXiv:0901.2258 [hep-th]

  12. R. Banerjee, S.K. Modak, Quantum tunneling, blackbody spectrum and non-logarithmic entropy correction for Lovelock black holes. J. High Energy Phys. 0911, 073 (2009). arXiv:0908.2346 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  13. R. Banerjee, S. Gangopadhyay, S.K. Modak, Voros product, noncommutative Schwarzschild black hole and corrected area law. Phys. Lett. B 686, 181 (2010). arXiv:0911.2123 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  14. D.V. Fursaev, Temperature and entropy of a quantum black hole and conformal anomaly. Phys. Rev. D 51, R5352 (1995). arXiv:hep-th/9412161

    Article  MathSciNet  ADS  Google Scholar 

  15. R.B. Mann, S.N. Solodukhin, Universality of quantum entropy for extreme black holes. Nucl. Phys. B 523, 293 (1998). arXiv:hep-th/9709064

    Article  MATH  MathSciNet  ADS  Google Scholar 

  16. S. Das, P. Majumdar, R.K. Bhaduri, General logarithmic corrections to black hole entropy. Class. Quantum Gravity 19, 2355 (2002). arXiv:hep-th/0111001

    Article  MATH  MathSciNet  ADS  Google Scholar 

  17. S.S. More, Higher order corrections to black hole entropy. Class. Quantum Gravity 22, 4129 (2005). gr-qc/0410071

    Article  MATH  MathSciNet  ADS  Google Scholar 

  18. S. Mukherjee, S.S. Pal, Logarithmic corrections to black hole entropy and AdS/CFT correspondence. J. High Energy Phys. 0205, 026 (2002). arXiv:hep-th/0205164

    Article  ADS  Google Scholar 

  19. S. Carlip, Logarithmic corrections to black hole entropy from the Cardy formula. Class. Quantum Gravity 17, 4175 (2000). arXiv:gr-qc/0005017

    Article  MATH  MathSciNet  ADS  Google Scholar 

  20. M.R. Setare, Logarithmic correction to the Cardy-Verlinde formula in Achucarro-Ortiz black hole. Eur. Phys. J. C 33 (2004). arXiv:hep-th/0309134

  21. G. Hooft, The scattering matrix approach for the quantum black hole: an overview. Int. J. Mod. Phys. A 11, 4623 (1996). arXiv:gr-qc/9607022

    Article  MATH  ADS  Google Scholar 

  22. D.N. Page, Hawking radiation and thermodynamics of black holes. New J. Phys. 7, 203 (2005). arXiv:hep-th/0409024

    Article  MathSciNet  ADS  Google Scholar 

  23. S. Sarkar, S. Shankaranarayanan, L. Sriramkumar, Sub-leading contributions to the black hole entropy in the brick wall approach. Phys. Rev. D 78, 024003 (2008). arXiv:0710.2013 [gr-qc]

    Article  MathSciNet  ADS  Google Scholar 

  24. H. Rawson, Inorganic Glass Forming Systems (Academic Press, New York, 1967)

    Google Scholar 

  25. J. Wong, C.A. Angell, Glass Structure by Spectroscopy (Dekker, New York, 1976)

    Google Scholar 

  26. B.C. Giessen, C.N. Wagner, Liquid metals, in: ed. by S.Z. Beer Chemistry and Physics (Dekker, New York, 2010)

    Google Scholar 

  27. P.K. Gupta, C.T. Moynihan, Prigogine-Defay ratio for systems with more than one order parameter. J. Chem. Phys. 65, 4136 (1976)

    Article  ADS  Google Scholar 

  28. C.T. Moynihan, A.V. Lesikar, Ann. N.Y. Acad. Sci. 371, 151 (1981)

    ADS  Google Scholar 

  29. S.W. Hawking, D.N. Page, Thermodynamics of black holes in anti-de Sitter space. Commun. Math. Phys. 87, 577 (1983)

    Article  MathSciNet  ADS  Google Scholar 

  30. M. Cvetic, S. Nojiri, S.D. Odintsov, Black hole thermodynamics and negative entropy in de Sitter and anti-de Sitter Einstein–Gauss–Bonnet gravity. Nucl. Phys. B 628, 295 (2002). arXiv:hep-th/0112045

    Article  MATH  MathSciNet  ADS  Google Scholar 

  31. S. Nojiri, S.D. Odintsov, Anti-de Sitter black hole thermodynamics in higher derivative gravity and new confining-deconfining phases in dual CFT. Phys. Lett. B 521, 87 (2001). Erratum-ibid. 542, 301 (2002). arXiv:hep-th/0109122

    Article  MATH  MathSciNet  ADS  Google Scholar 

  32. S. Stotyn, R. Mann, Phase transitions between solitons and black holes in asymptotically AdS/Z k spaces. Phys. Lett. B 681, 472 (2009). arXiv:0909.0919v1 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  33. R.G. Cai, S.P. Kim, B. Wang, Ricci flat black holes and Hawking–Page phase transition in Gauss–Bonnet gravity and dilaton gravity. Phys. Rev. D 76, 024011 (2007). arXiv:0705.2469 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  34. D. Anninos, G. Pastras, Thermodynamics of the Maxwell–Gauss–Bonnet anti-de Sitter black hole with higher derivative gauge corrections. J. High Energy Phys. 0907, 030 (2009). arXiv:0807.3478 [hep-th]

    Article  ADS  Google Scholar 

  35. U. Gursoy, E. Kiritsis, L. Mazzanti, F. Nitti, Holography and thermodynamics of 5D dilaton-gravity. J. High Energy Phys. 0905, 033 (2009). arXiv:0812.0792 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  36. Y.S. Myung, Y.W. Kim, Y.J. Park, Thermodynamics and phase transitions in the Born–Infeld–anti-de Sitter black holes. Phys. Rev. D 78, 084002 (2008). arXiv:0805.0187 [gr-qc]

    Article  MathSciNet  ADS  Google Scholar 

  37. G. Ishiki, S.W. Kim, J. Nishimura, A. Tsuchiya, Testing a novel large-N reduction for N=4 super Yang–Mills theory on R×S 3. J. High Energy Phys. 0909, 029 (2009). arXiv:0907.1488 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. S.N. Bose National Centre for Basic Sciences, JD Block, Sector III, Salt Lake, Kolkata, 700098, India

    Rabin Banerjee & Sujoy Kumar Modak

  2. Narasinha Dutt College, 129, Belilious Road, Howrah, 711101, India

    Saurav Samanta

Authors
  1. Rabin Banerjee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sujoy Kumar Modak
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Saurav Samanta
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Saurav Samanta.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Banerjee, R., Modak, S.K. & Samanta, S. Glassy phase transition and stability in black holes. Eur. Phys. J. C 70, 317–328 (2010). https://doi.org/10.1140/epjc/s10052-010-1443-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjc/s10052-010-1443-y

Keywords

Search

Navigation