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Geometrothermodynamics of black holes with a nonlinear source

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Abstract

We study thermodynamics and geometrothermodynamics of a particular black hole configuration with a nonlinear source. We use the mass as fundamental equation, from which it follows that the curvature radius must be considered as a thermodynamic variable, leading to an extended equilibrium space. Using the formalism of geometrothermodynamics, we show that the geometric properties of the thermodynamic equilibrium space can be used to obtain information about thermodynamic interaction, critical points and phase transitions. We show that these results are compatible with the results obtained from classical black hole thermodynamics.

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References

  1. 1.

    Ayon-Beato, E., Garcia, A.: New regular black hole solution from nonlinear electrodynamics. Phys. Lett. B 464, 25 (1999)

    MathSciNet  Article  ADS  Google Scholar 

  2. 2.

    Bronnikov, K.A.: Regular magnetic black holes and monopoles from nonlinear electrodynamics. Phys. Rev. D 63, 044005 (2001)

    MathSciNet  Article  ADS  Google Scholar 

  3. 3.

    Hassaine, M., Martinez, C.: Higher-dimensional charged black hole solutions with a nonlinear electrodynamics source. Class. Quantum Gravit. 25, 19, 5023 (2008)

  4. 4.

    Hassaine, M., Martinez, C.: Higher-dimensional black holes with a conformally invariant Maxwell source. Phys. Rev. D 75, 027502 (2007)

    MathSciNet  Article  ADS  Google Scholar 

  5. 5.

    Hendi, S.H., Rastegar-Sedehi, H.R.: Ricci flat rotating black branes with a conformally invariant Maxwell source. Gen. Relativ. Gravit. 41, 1355 (2009)

    MathSciNet  Article  ADS  Google Scholar 

  6. 6.

    Maeda, H., Hassaine, M., Martinez, C.: Magnetic black holes with higher-order curvature and gauge corrections in even dimensions. JHEP 1008, 123 (2010)

    Article  ADS  Google Scholar 

  7. 7.

    Kats, Y., Motl, L., Padi, M.: Higher-order corrections to mass-charge relation of extremal black holes. JHEP 0712, 068 (2007)

    MathSciNet  Article  ADS  Google Scholar 

  8. 8.

    Maldacena, J.M.: The Large N limit of superconformal field theories and supergravity. Int. J. Theor. Phys. 38, 1113 (1999)

    MathSciNet  Article  Google Scholar 

  9. 9.

    Hawking, S.W., Page, D.N.: Thermodynamics of black holes in anti-de Sitter space. Commun. Math. Phys. 87, 577–588 (1983)

    MathSciNet  Article  ADS  Google Scholar 

  10. 10.

    Chamblin, A., Emparan, R., Johnson, C.V., Myers, R.C.: Charged AdS black holes and catastrophic holography. Phys. Rev. D 60, 064018 (1999)

    MathSciNet  Article  ADS  Google Scholar 

  11. 11.

    Kastor, D., Ray, S., Traschen, J.: Enthalpy and the mechanics of AdS black holes. Class. Quant. Grav. 26, 195011 (2009)

    MathSciNet  Article  ADS  Google Scholar 

  12. 12.

    Dolan, B.P.: The cosmological constant and the black hole equation of state. Class. Quant. Grav. 28, 125020 (2011)

    Article  ADS  Google Scholar 

  13. 13.

    Davies, P.C.W.: Thermodynamics of black holes. Proc. R. Soc. Lond. A 353, 499 (1977)

    Article  ADS  Google Scholar 

  14. 14.

    Weinhold, F.: J. Chem. Phys. 63, 2479, 2484, 2488, 2496 (1975)

  15. 15.

    Weinhold, F.: J. Chem. Phys. 65, 558 (1976)

    Article  ADS  Google Scholar 

  16. 16.

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

    Article  ADS  Google Scholar 

  17. 17.

    Quevedo, H.: Geometrothermodynamics. J. Math. Phys. 48, 013506 (2007)

    MathSciNet  Article  ADS  Google Scholar 

  18. 18.

    Arciniega, G., Sánchez, A.: Geometric description of the thermodynamics of a black hole with power Maxwell invariant source. arXiv:1404.6319v1 [math-ph] (2014)

  19. 19.

    Quevedo, H., Quevedo, M.N., Sánchez, A.: Homogeneity and thermodynamic identities in geometrothermodynamics. Eur. Phys. J. C 77, 158 (2017)

    Article  ADS  Google Scholar 

  20. 20.

    Hendi, S.H., Vahidinia, M.H.: Extended phase space thermodynamics and P-V criticality of black holes with a nonlinear source. Phys. Rev. D 88, 084045 (2013)

    Article  ADS  Google Scholar 

  21. 21.

    Quevedo, H., Quevedo, M.N., Sánchez, A.: Quasi-homogeneous black hole thermodynamics. Eur. Phys. J. C 79, 229 (2019)

    Article  ADS  Google Scholar 

  22. 22.

    Teitelboim, C.: The cosmological constant as a thermodynamic black hole parameter. Phys. Lett. B 158, 293–297 (1985)

    Article  ADS  Google Scholar 

  23. 23.

    Caldarelli, M.M., Cognola, G., Klemm, D.: Thermodynamics of Kerr–Newman–AdS black holes and conformal field theories. Class. Quant. Grav. 17, 399–420 (2000)

    MathSciNet  Article  ADS  Google Scholar 

  24. 24.

    Altamirano, N., Kubizňák, D., Mann, R.B., Sherkatghanad, Z.: Thermodynamics of rotating black holes and black rings: phase transitions and thermodynamic volume. Galaxies 2, 89–159 (2014)

    Article  ADS  Google Scholar 

  25. 25.

    Cvetic, M., Gibbons, G.W., Kubizňák, D., Pope, C.N.: Black hole enthalpy and an entropy inequality for the thermodynamic volume. Phys. Rev. D 84, 024037 (2011)

    Article  ADS  Google Scholar 

  26. 26.

    Dolan, B.P., Kastor, D., Kubizňák, D., Mann, R.B., Traschen, J.: Thermodynamic volumes and isoperimetric inequalities for de Sitter black holes. Phys. Rev. D 87, 104017 (2013)

    Article  ADS  Google Scholar 

  27. 27.

    Callen, H.B.: Thermodinamics. Wiley, New York (1981)

    Google Scholar 

  28. 28.

    Kubizňák, D., Mann, R.B : P–V criticality of charged AdS black holes. J. High Energy Phys. 2012, 33 (2012). https://doi.org/10.1007/JHEP07(2012)033

  29. 29.

    Arnold, V.I.: Mathematical Methods of Classical Mechanics. Springer, New York (1980)

    Google Scholar 

  30. 30.

    Quevedo, H., Sanchez, A., Taj, S., Vazquez, A.: Phase transitions in geometrothermodynamics. Gen. Relativ. Gravit. 43, 1153 (2011)

    MathSciNet  Article  ADS  Google Scholar 

  31. 31.

    Wei, S.W., Liu, Y.X., Mann, R.B.: Ruppeiner geometry, phase transitions, and the microstructure of charged AdS black holes. Phys. Rev. D 100, 124033 (2019)

    MathSciNet  Article  ADS  Google Scholar 

  32. 32.

    Oshima, H., Obata, T., Hara, H.: Riemann scalar curvature of ideal quantum gases obeying Gentile’s statistics. J. Phys. A: Math. Gen. 32, 6373 (1999)

    MathSciNet  Article  ADS  Google Scholar 

  33. 33.

    Dolan, B. P.: Where is the PdV term in the first law of black hole thermodynamics? arXiv:1209.1272 [gr-qc] (2016)

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Acknowledgements

This work was partially supported by Conacyt-Mexico, Grant No. A1-S-31269, and by UNAM-DGAPA-PAPIIT, Grant No. 114520.

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Correspondence to Alberto Sánchez.

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Sánchez, A. Geometrothermodynamics of black holes with a nonlinear source. Gen Relativ Gravit 53, 71 (2021). https://doi.org/10.1007/s10714-021-02843-x

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Keywords

  • Thermodynamics
  • Thermodynamic functions and equations of state
  • Phase transition
  • Riemannian geometries