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Thermodynamic Studies with Higher-Order Quantum Corrected Entropy: Higher Dimensional Gauss-Bonnet Black Holes

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Abstract

In addition to the classical definition of the black hole’s entropy, quantum mechanics requires several modifications of it. In this article, we consider the higher-order quantum correction in entropy and analyze the thermodynamic properties of a black hole solution which is sitting in one of the modified gravity theories, viz. Gauss-Bonnet gravity, in this point of view. Here mainly two thermodynamic potentials, Gibbs free energy and Helmholtz free energy are studied. As both potentials are very much important to investigate small/large black hole phase transition. Presenting the variations of higher-order corrected Gibbs free energy and Helmholtz free energy in different conditions, we analyze the phase transition and critical behavior of said black holes. We also re-examine our results, with the \(P-V\) criticality analyses and study \(P-r_+\) diagrams. Moreover, we compute the critical temperature, pressure and volume and the relation among them. Here we find an interesting result for \(Q=0\) and for the Ricci flat horizon of this black hole that the relation is exactly equal to the result obtained for the van der Waals system. Further, we study thermal stability by computing the specific heat with higher-order correction and explain it by depicting the \(C_{HC}\) vs \(r_+\) diagrams in different conditions.

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Data Availibility Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: Since no datasets were generated or analyzed during the current study, data sharing does not apply to this article.]

References

  1. Hawking, S.W., Ellis, G.F.R.: The large scale structure of spacetime. Cambridge University Press, Cambridge (1973)

    Book  MATH  Google Scholar 

  2. Hawking, S.W., Penrose, R.: The nature of space and time. Princeton University Press, Princeton (1996)

    MATH  Google Scholar 

  3. Bekenstein, J.D.: Transcendence of the law of Baryon-number conservation in black-hole physics. Phys. Rev. Letters 28, 452 (1972) [SPIRES]. Phys. Rev. D 5, 1239, 2403 (1972)

  4. Hawking, S.W.: Particle creation by black holes. Commun Math. Phys. 43, 199 (1975)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Bekenstein, J.D.: Extraction of energy and charge from a black hole. Phys. Rev. D 7, 949 (1973)

    Article  ADS  Google Scholar 

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

  7. Susskind, L.: The world as a hologram. J. Math. Phys. 36, 6377 (1995)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. Bousso, R.: The holographic principle. Rev. Mod. Phys. 74, 825 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. Rama, S.K.: Holographic principle in the closed universe: a resolution with negative pressure matter. Phys. Lett. B 457, 268 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. Bak, D., Rey, S.J.: Cosmic holography. Class. Quantum Grav. 17, L83 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  11. Das, S., Majumdar, P., Bhaduri, R.K.: General logarithmic corrections to black hole entropy. Class. Quantum. Grav. 19, 2355 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. Xu, W., Zhao, L.: Charged black hole with a scalar hair in (2+1) dimensions. Phys. Rev. D 87, 124008 (2013)

    Article  ADS  Google Scholar 

  13. Sadeghi, J., Pourhassan, B., Pourasadollah, F.: Holographic Brownian motion in 2 + 1 dimensional hairy black holes. Eur. Phys. J. C 74, 2793 (2014)

    Article  ADS  Google Scholar 

  14. Naji, J.: Energy loss of a heavy particle near 3D charged rotating hairy black hole. Eur. Phys. J. C 74, 2697 (2014)

    Article  ADS  Google Scholar 

  15. Pourhassan, B.: The Klein–Gordon equation of a rotating charged hairy black hole in (2 + 1) dimensions. Mod. Phys. Lett. A 31, 1650057 (2016)

  16. Pourhassan, B., Faizal, M.: Thermal fluctuations in a charged AdS black hole. Europhys. Lett. 111, 40006 (2015)

    Article  ADS  Google Scholar 

  17. Govindarajan, T.R., Kaul, R.N., Suneeta, V.: Quantum Gravity on \(dS_{3}\). Class. Quant. Grav. 19, 4195 (2004)

    Article  ADS  MATH  Google Scholar 

  18. Upadhyay, S., Pourhassan, B., Farahani, H.: P-V criticality of first-order entropy corrected AdS black holes in massive gravity. Phys. Rev. D 95, 106014 (2017). arXiv:1704.01016 (2017)

  19. Pourdarvish, A., Sadeghi, J., Farahani, H., Pourhassan, B.: Thermodynamics and statistics of Gödel black hole with logarithmic correction’. Theor. Phys. 52, 3560 (2013)

    Article  MATH  Google Scholar 

  20. Pourhassan, B., Upadhyay, S., Saadat, H., Farahani, H.: Quantum gravity effects on Horava-Lifshitz black hole. Nucl. Phys. B 928, 415 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  21. Upadhyay, S.: Quantum corrections to thermodynamics of quasitopological black holes. Phys. Lett. B 775, 130 (2017)

    Article  ADS  Google Scholar 

  22. Pourhassan, B., Faizal, M., Upadhyay, S., Asfar, L.A.: Thermal fluctuations in a hyperscaling-violation background. Eur. Phys. J. C 77, 555 (2017)

    Article  ADS  Google Scholar 

  23. Upadhyay, S., Pourhassan, B., Farahani, H.: \(P-V\) criticality of first-order entropy corrected AdS black holes in massive gravity. Phys. Rev. D 95, 106014 (2017)

  24. Upadhyay, S.: Leading-order corrections to charged rotating AdS black holes thermodynamics. Gen. Relativ. Gravit. 50, 128 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. Nadeem-ul-islam, Prince A., Ganai Upadhyay, S.: Thermal fluctuations to thermodynamics of non-rotating BTZ black hole. Prog. Theor. Exp. Phys. 103B06 (2019). arXiv:1811.05313

  26. Upadhyay, S., Hendi, S.H., Panahiyna, S., Panah, B.E.: Thermal fluctuations of charged black holes in gravity’s rainbow. Prog. Theor. Exp. Phys. 2018, 093E01 (2018). arXiv:1809.01078

  27. Upadhyay, S., Soroushfar, S., Saffari, R.: Perturbed thermodynamics and thermodynamic geometry of a static black hole in f(R) gravity. Mod. Phys. Lett. A 36, 2150212 (2023). arXiv:1801.09574

  28. Pourhassan, B., Faizal, M., Debnath, U.: Effects of thermal fluctuations on the thermodynamics of modified Hayward black hole. Eur. Phys. J. C 76, 145 (2016)

    Article  ADS  Google Scholar 

  29. Faizal, M., Pourhassan, B.: Correction terms for the thermodynamics of a black Saturn. Phys. Lett. B 751, 487 (2015)

    Article  ADS  MATH  Google Scholar 

  30. Pourhassan, B., Faizal, M.: Effect of thermal fluctuations on a charged dilatonic black Saturn. Phys. Lett. B 755, 444 (2016)

    Article  ADS  MATH  Google Scholar 

  31. Pourhassan, B., Faizal, M.: Thermodynamics of a sufficient small singly spinning Kerr-AdS black hole. Nucl. Phys. B 913, 834 (2016)

    Article  ADS  MATH  Google Scholar 

  32. Pourhassan, B., Farahani, H., Upadhyay, S.: Thermodynamics of higher-order entropy corrected Schwarzschild-Beltrami-de Sitter black hole. Int. J. Mod. Phys. A 34, 1950158 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  33. Sadeghi, J., Pourhassan, B., Rahimi, F.: Logarithmic corrections of charged hairy black hole in (2+1) dimension. Can. J. Phys. 92, 1638 (2014)

    Article  ADS  Google Scholar 

  34. S. Upadhyay, S., Pourhassan, B.: Logarithmic corrected Van der Waals black holes in higher dimensional AdS space. Prog. Theor. Exp. Phys. 2019, 013B03 (2019). arXiv:1711.04254

  35. Haldar, A., Biswas, R.: Thermodynamic variables of first-order entropy corrected Lpvelock-AdS black holes: \(P-V\) criticality analysis. Gen. Relativ. Grav. 50, 69 (2018)

  36. Haldar, A., Biswas, R.: Geometrothermodynamic analysis and \(P-V\) criticality of higher dimensional charged Gauss-Bonnet black holes with first order entropy correction. Gen. Relativ. Grav. 51, 35 (2019)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  37. Tawfik, A.N., El Dahab, E.A.: Corrections to entropy and thermodynamics of charged black hole using generalized uncertainty principle. Int. J. Mod. Phys. A 30, 1550030 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  38. Feng, Z.W., Li, H.L., Zu, X.T., Yang, S.Z.: Quantum corrections to the thermodynamics of Schwarzschild-Tangherlini black hole and the generalized uncertainty principle. Eur. Phys. J. C 76, 212 (2016)

    Article  ADS  Google Scholar 

  39. Upadhyay, S., Nadeem-ul-islam., Ganai P.A.: A modified thermodynamics of rotating and charged BTZ black hole. JHAP 2, 25 (2022)

  40. Saghafi, S., Nozari, K.: Shadow behavior of the quantum-corrected Schwarzschild black hole immersed in holographic quintessence. J. Hologr App. Phys. 2, 31–38 (2022)

    Google Scholar 

  41. Chatterjee, A., Ghosh, A.: Exponential corrections to black hole entropy. Phys. Rev. Lett. 125, 041302 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  42. Pourhassan, B.: Exponential corrected thermodynamics of black holes. J. Stat. Mech. 2021, 073102 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  43. Cai, R.G., Cao, L.M., Li, L., Yang, R.Q.: \(P-V\) criticality in the extended phase space of Gauss-Bonnet black holes in AdS space. J. High Energy Phys. 9, 1–22 (2013). arXiv:1306.6233

  44. Guo, X-Y., Li, H-F., Zhang, L-C.: Entropy of higher dimensional charged Gauss-Bonnet Black hole in de Sitter Space. Commun. Theor. Phys. 72, 085403 (2020). arXiv:1803.09456 (2018)

  45. Kumar, A., Singh, D.V., Ghosh, S.G.: Hayward black holes in Einstein-Gauss-Bonnet gravity. Ann. Phys. 413, 168214 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  46. Shahraeini, S., Nozari, K., Sagha, S.: Radiation from Hayward black hole via tunneling process in Einstein-Gauss-Bonnet gravity. J. Hologr. App. Phys. 2, 55–62 (2022)

    Google Scholar 

  47. Kubiznak, D., Mann, R.B.: P-V criticality of charged AdS black holes. J. High Energ. Phys. 1207, 033 (2012). arXiv:1205.0559

    Article  ADS  MathSciNet  MATH  Google Scholar 

  48. Kastor, D., Ray, S., Traschen, J.: Enthalpy and the Mechanics of AdS Black Holes. Class. Quant. Grav. 26,(2009). arXiv:0904.2765

  49. Bodendorfer, N., Neiman, Y.: Wald entropy formula and loop quantum gravity. Phys. Rev. D 90, 084054 (2014)

    Article  ADS  Google Scholar 

  50. Mahapatra, S.: Logarithmic black hole entropy corrections and holographic Rényi entropy. Eur. Phys. J. C 78, 23 (2018)

    Article  ADS  Google Scholar 

  51. Gibbons, G.W., Hawking, S.W.: Action integrals and partition functions in quantum gravity. Phys. Rev. D 15, 2752 (1976)

    Article  ADS  Google Scholar 

  52. More, S.S.: Higher order corrections to black hole entropy. Class. Quant. Grav. 22, 4129 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  53. Govindarajan, T.R., Kaul, R.K., V Suneeta, V.: Logarithmic correction to the Bekenstein-Hawking entropy of the BTZ black hole. Class. Quantum Grav. 18, 2877 (2001)

  54. Liu, H., Meng, X.-H.: Thermodynamics of Schwarzschild-Beltrami-de Sitter Black Hole. Mod. Phys. Lett. A 32, 1750146 (2017). arXiv:1611.03604

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Acknowledgements

Amritendu Haldar wishes to thank the Department of Physics, the University of Burdwan for the research facilities provided during the work.

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  1. Department of Physics, Sripat Singh College, Jiaganj, Murshidabad, 742123, India

    Amritendu Haldar

  2. Department of Physics, Nabagram Hiralal Paul College, Nabagram (Konnagar), Hoogly, 712246, India

    Anendu Haldar

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Amritendu Haldar wrote the main manuscript text and Anendu Haldar prepared all figures and explained them. All authors reviewed the manuscript.

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Haldar, A., Haldar, A. Thermodynamic Studies with Higher-Order Quantum Corrected Entropy: Higher Dimensional Gauss-Bonnet Black Holes. Int J Theor Phys 62, 223 (2023). https://doi.org/10.1007/s10773-023-05478-7

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