Effect of thermal fluctuation on the thermodynamics of GMGHS black hole

Abstract

In present paper we discuss the effect of higher order corrections of entropy on the thermodynamic fluctuation of the Gibbons-Maeda-Garfinkle-Horowitz-Strominger black hole (GMGHS), i.,e. charged diatonic black hole. By investigating the thermodynamic property functions, such as the internal energy, the enthalpy, the Helmholtz free energy, the Gibbs free energy and the heat capacity, we find that the correction from the thermodynamic fluctuation is very important for small black hole case and one can neglect the correction for large black hole case. We also find that when there is no thermal fluctuation, this black hole thermodynamic system acts as an ideal gas state. However when we consider the thermal fluctuation, we can see the Van der waals type behavior in GMGHS black hole system. Finally, we discuss the stability of GMGHS black hole by investigating the behaviour of heat capacity under effect of thermal fluctuation, we find that, without any thermal fluctuation, we get the completely unstable black hole. However, with the presence of thermal fluctuation, the black hole becomes stable at smaller value of horizon radius, also there is a stable to unstable phase transition from the corrected specific heat.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant Nos. U1731107.

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Correspondence to Juhua Chen.

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Chen, X., Huang, X., Chen, J. et al. Effect of thermal fluctuation on the thermodynamics of GMGHS black hole. Gen Relativ Gravit 53, 9 (2021). https://doi.org/10.1007/s10714-020-02780-1

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Keywords

  • Thermal fluctuation
  • GMGHS black hole
  • Thermodynamics