Phase transitions and geometrothermodynamics of regular black holes

  • R. Tharanath
  • Jishnu Suresh
  • V. C. Kuriakose
Research Article


In this paper we study the thermodynamics and state space geometry of a set of regular black hole solutions such as Bardeen black hole (1968), Ayón-Beato and García black hole (Phys Rev Lett 80:5056, 1998), Hayward black hole (Phys Rev Lett 96:031103, 2006) and Berej–Matyjasek–Trynieki–Wornowicz black hole (Gen Relativ Gravit 38(5):885906, 2006). We find that all these black holes show second order thermodynamic phase transitions by observing discontinuities in heat capacity–entropy graphs as well as the cusp type double point in free energy–temperature graph. Using the formulation of geometrothermodynamics we again find the singularities in the heat capacity of the black holes by calculating the curvature scalar of the Legendre invariant metric.


Black holes Phase transition Geoemtrothermodynamics 



T.R. wishes to thank UGC, New Delhi for financial support under RFSMS scheme. J.S. and V.C.K. wishes to thank UGC, for the financial support through a major research Project sanctioned to V.C.K. V.C.K. also wishes to acknowledge Associateship of IUCAA, Pune, India.


  1. 1.
    Bardeen, J.: Proceedings of GR5. Tiflis, U.S.S.R (1968)Google Scholar
  2. 2.
    Ayón-Beato, E., García, A.: Phys. Rev. Lett. 80, 5056 (1998)CrossRefADSGoogle Scholar
  3. 3.
    Borde, A.: Phys. Rev. D 50, 3692 (1994)CrossRefADSMathSciNetGoogle Scholar
  4. 4.
    Borde, A.: Phys. Rev. D 55, 7615 (1997)CrossRefADSMathSciNetGoogle Scholar
  5. 5.
    Berej, W., Matyjasek, J., Tryniecki, D., Woronowicz, M.: Gen. Relativ. Gravit. 38(5), 885906 (2006)MathSciNetGoogle Scholar
  6. 6.
    Hayward, S.A.: Phys. Rev. Lett. 96, 031103 (2006)CrossRefADSGoogle Scholar
  7. 7.
    Zhou, S., Chen, J., Wang, Y.: arxiv:1112.5909
  8. 8.
    Eiroa, E.F., sendra, C.M.: Class. Quantum Gravity 28, 085008 (2011)CrossRefADSMathSciNetGoogle Scholar
  9. 9.
    Moreno, C., Sarbach, O.: Phys. Rev. D 67, 024028 (2003)CrossRefADSMathSciNetGoogle Scholar
  10. 10.
    Fernando, S., Correa, J.: Phys. Rev. D 86, 064039 (2012)CrossRefADSGoogle Scholar
  11. 11.
    Akbar, M., Salem, N., Hussein, S.A.: Chin. Phys. Lett. 29(7), 070401 (2012)CrossRefADSGoogle Scholar
  12. 12.
    Tharanath, R., Kuriakose, V.C.: Mod. Phys. Lett. A 28, 4 (2013)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Tharanath, R., Varghese, N., Kuriakose, V.C.: Mod. Phys. Lett. A 29, 11 (2014)CrossRefGoogle Scholar
  14. 14.
    Hermann, R.: Geometry, Physics and Systems. Marcel Dekker, New York (1973)zbMATHGoogle Scholar
  15. 15.
    Mrugala, R.: Phys. A (Amsterdam) 125, 631 (1984)CrossRefADSMathSciNetGoogle Scholar
  16. 16.
    Weinhold, F.: J. Chem. Phys. 63, 2479 (1975)CrossRefADSMathSciNetGoogle Scholar
  17. 17.
    Ruppeiner, G.: Phys. Rev. A. 20, 1608 (1979)CrossRefADSGoogle Scholar
  18. 18.
    Quevedo, H.: J. Math. Phys. (N.Y.) 48, 013506 (2007)CrossRefADSMathSciNetGoogle Scholar
  19. 19.
    Quevedo, H.: Gen. Relativ. Gravit. 40, 971 (2008)CrossRefADSzbMATHMathSciNetGoogle Scholar
  20. 20.
    Quevedo, H., Vazquez, A.: Recent developments in gravitation and cosmology. In: Macias, A., Lämmerzahl, C., Camacho, A. (eds.) AIP Conference on Proceedings No. 977. AIP, New York (2008)Google Scholar
  21. 21.
    Suresh, J., Tharanath, R., Varghese, N., Kuriakose, V.C.: Eur. Phys. J. C 74, 2819 (2014)CrossRefADSGoogle Scholar
  22. 22.
    Tharanath, R., Suresh, J., Varghese, N., Kuriakose, V.C.: Gen. Relativ. Gravit. doi: 10.1007/s10714-014-1743-x
  23. 23.
    Rasheed, D.A.: Non-linear electrodynamics: zeroth and first law of Black hole mechanics. hep-th/9901133 (1999)
  24. 24.
    Ayón-Beato, E., García, A.: Phys. Lett. B 464, 25 (1999)CrossRefADSzbMATHMathSciNetGoogle Scholar
  25. 25.
    Ayón-Beato, E., García, A.: Gen. Relativ. Gravit. 31, 629 (1999)CrossRefADSzbMATHGoogle Scholar
  26. 26.
    Ayón-Beato, E., García, A.: Phys. Lett. B 493, 149 (2000)CrossRefADSzbMATHMathSciNetGoogle Scholar
  27. 27.
    Ayón-Beato, E., García, A.: Gen. Relativ. Gravit. 37, 635 (2005)CrossRefADSzbMATHGoogle Scholar
  28. 28.
    Callen, H.B.: Thermodynamics and an Introduction to Thermostatics. Wiley, New York (1985)Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of PhysicsCochin University of Science and TechnologyCochinIndia

Personalised recommendations