# Impact of Thermal Fluctuations on Logarithmic Corrected Massive Gravity Charged Black Hole

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## Abstract

**:**

## 1. Introduction

## 2. Thermal Corrections of Logarithmic Charged Black Hole in Massive Gravity

**F**is hypergeometric function and ${m}_{0}$ is related to the total mass of the BH. q is a constant, which represents the total charge of BH.

## 3. Holographic Duality and Thermal Stability

## 4. Concluding Remarks

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

## Appendix B

## Appendix C

## Appendix D

## References

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**Figure 1.**The corrected entropy of logarithmic charged BH in MG. We set $\beta =1$, $n=3$, ${c}_{0}=1$, ${c}_{1}=1$, ${c}_{2}=1$, ${c}_{3}=1$ and ${c}_{4}=1$.

**Figure 2.**The corrected entropy of logarithmic charged BH in MG. We set $\beta =1$, $n=3$, ${c}_{0}=1$, ${c}_{1}=1$, ${c}_{2}=1$, ${c}_{3}=1$ and ${c}_{4}=1$.

**Figure 3.**The corrected entropy of logarithmic charged BH in MG. We set $\beta =1$, ${c}_{0}=1$, ${c}_{1}=1$, ${c}_{2}=1$, ${c}_{3}=1$ and ${c}_{4}=1$.

**Figure 4.**The corrected entropy of logarithmic charged BH in MG. We set $n=3$, ${c}_{0}=1$, ${c}_{1}=1$, ${c}_{2}=1$, ${c}_{3}=1$ and ${c}_{4}=1$.

**Figure 5.**The HFE of logarithmic charged BH in MG. We set $n=3$, ${c}_{0}=1$, ${c}_{1}=1$, ${c}_{2}=1$, ${c}_{3}=1$ and ${c}_{4}=1$.

**Figure 6.**The HFE of logarithmic charged BH in MG. We set $n=3$, ${c}_{0}=1$, ${c}_{1}=1$, ${c}_{2}=1$, ${c}_{3}=1$ and ${c}_{4}=1$.

**Figure 7.**The HFE of logarithmic charged BH in MG. We set $\beta =1$, ${c}_{0}=1$, ${c}_{1}=1$, ${c}_{2}=1$, ${c}_{3}=1$ and ${c}_{4}=1$.

**Figure 8.**The HFE of logarithmic charged BH in MG. We set $n=3$, ${c}_{0}=1$, ${c}_{1}=1$, ${c}_{2}=1$, ${c}_{3}=1$ and ${c}_{4}=1$.

**Figure 9.**The internal energy of logarithmic charged BH in MG. We set $n=3$, ${c}_{0}=1$, ${c}_{1}=1$, ${c}_{2}=1$, ${c}_{3}=1$ and ${c}_{4}=1$.

**Figure 10.**The internal energy of logarithmic charged BH in MG. We set $n=3$, ${c}_{0}=1$, ${c}_{1}=1$, ${c}_{2}=1$, ${c}_{3}=1$ and ${c}_{4}=1$.

**Figure 11.**The internal energy of logarithmic charged BH in MG. We set $\beta =3$, ${c}_{0}=1$, ${c}_{1}=1$, ${c}_{2}=1$, ${c}_{3}=1$ and ${c}_{4}=1$.

**Figure 12.**The internal energy of logarithmic charged BH in MG. We set $n=3$, ${c}_{0}=1$, ${c}_{1}=1$, ${c}_{2}=1$, ${c}_{3}=1$ and ${c}_{4}=1$.

**Figure 13.**The corrected pressure of logarithmic charged BH in MG. We set ${c}_{0}=1$, $\beta =1$, ${c}_{1}=1$, $n=3$, ${c}_{2}=1$, ${c}_{3}=1$ and ${c}_{4}=1$.

**Figure 14.**The corrected pressure of logarithmic charged BH in MG. We set $\beta =1$, ${c}_{0}=1$, ${c}_{1}=1$, $\beta =3$, ${c}_{3}=1$, ${c}_{2}=1$ and ${c}_{4}=1$.

**Figure 15.**The corrected pressure of logarithmic charged BH in MG. We set $n=3$, ${c}_{0}=1$, ${c}_{1}=1$, ${c}_{2}=1$, ${c}_{3}=1$ and ${c}_{4}=1$.

**Figure 16.**The enthalpy of logarithmic charged BH in MG. We set $n=3$, ${c}_{0}=1$, $\beta =1$, ${c}_{2}=1$, ${c}_{3}=1$, ${c}_{1}=1$, and ${c}_{4}=1$.

**Figure 17.**The enthalpy of logarithmic charged BH in MG. We set ${c}_{0}=1$, ${c}_{1}=1$, $\beta =1$, $n=3$, ${c}_{3}=1$, ${c}_{2}=1$, and ${c}_{4}=1$.

**Figure 18.**The enthalpy of logarithmic charged BH in MG. We set $k=1$, ${c}_{0}=1$, $\beta =1$, ${c}_{2}=1$, ${c}_{1}=1$, ${c}_{3}=1$ and ${c}_{4}=1$.

**Figure 19.**The enthalpy of logarithmic charged BH in MG. We set $k=1$, ${c}_{0}=1$, ${c}_{1}=1$, $n=3$, ${c}_{3}=1$, ${c}_{2}=1$, and ${c}_{4}=1$.

**Figure 20.**The Gibbs free energy of logarithmic charged BH in MG. We set ${c}_{0}=1$, ${c}_{1}=1$, $k=1$, ${c}_{2}=1$, $n=3$, ${c}_{3}=1$ and ${c}_{4}=1$.

**Figure 21.**The Gibbs free energy of logarithmic charged BH in MG. We set $n=3$, ${c}_{0}=1$, $\beta =1$, ${c}_{2}=1$, ${c}_{1}=1$, ${c}_{3}=1$ and ${c}_{4}=1$.

**Figure 22.**The Gibbs free energy of logarithmic charged BH in MG. We set $k=1$, $\beta =1$, ${c}_{0}=1$, ${c}_{1}=1$, ${c}_{2}=1$, ${c}_{3}=1$ and ${c}_{4}=1$.

**Figure 23.**The Gibbs free energy of logarithmic charged BH in MG. We set $k=1$, $n=3$, ${c}_{0}=1$, ${c}_{1}=1$, ${c}_{2}=1$, ${c}_{3}=1$ and ${c}_{4}=1$.

**Figure 24.**The plot of $\Delta P=P-{P}_{v}$ in terms of ${r}_{+}$. We set $n=3$, ${c}_{0}=1$, ${c}_{1}=1$, ${c}_{2}=1$, ${c}_{3}=1$ and ${c}_{4}=1$.

**Figure 25.**The plot of $\Delta P=P-{P}_{v}$ in terms of ${r}_{+}$. We set $k=1$, ${c}_{0}=1$, ${c}_{1}=1$, ${c}_{2}=1$, ${c}_{3}=1$ and ${c}_{4}=1$.

**Figure 26.**The plot of $\Delta P=P-{P}_{v}$ in terms of ${r}_{+}$. We set $n=3$, ${c}_{0}=1$, ${c}_{1}=1$, ${c}_{2}=1$, ${c}_{3}=1$ and ${c}_{4}=1$.

**Figure 27.**Specific heat of logarithmic charged BH in MG. We set $k=1$, $n=3$, ${c}_{0}=1$, ${c}_{1}=1$, ${c}_{2}=1$, ${c}_{3}=1$ and ${c}_{4}=1$.

**Figure 28.**Specific heat of logarithmic charged BH in MG. We set $\beta =1$, $n=3$, ${c}_{0}=1$, ${c}_{1}=1$, ${c}_{2}=1$, ${c}_{3}=1$ and ${c}_{4}=1$.

**Figure 29.**Specific heat of logarithmic charged BH in MG. We set $\beta =1$, $k=1$, ${c}_{0}=1$, ${c}_{1}=1$, ${c}_{2}=1$, ${c}_{3}=1$ and ${c}_{4}=1$.

**Figure 30.**Specific heat of logarithmic charged BH in MG. We set $n=2$, $k=1$, ${c}_{0}=1$, ${c}_{1}=1$, ${c}_{2}=1$, ${c}_{3}=1$ and ${c}_{4}=1$.

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**MDPI and ACS Style**

Jawad, A.; Chaudhary, S.; Bamba, K.
Impact of Thermal Fluctuations on Logarithmic Corrected Massive Gravity Charged Black Hole. *Entropy* **2021**, *23*, 1269.
https://doi.org/10.3390/e23101269

**AMA Style**

Jawad A, Chaudhary S, Bamba K.
Impact of Thermal Fluctuations on Logarithmic Corrected Massive Gravity Charged Black Hole. *Entropy*. 2021; 23(10):1269.
https://doi.org/10.3390/e23101269

**Chicago/Turabian Style**

Jawad, Abdul, Shahid Chaudhary, and Kazuharu Bamba.
2021. "Impact of Thermal Fluctuations on Logarithmic Corrected Massive Gravity Charged Black Hole" *Entropy* 23, no. 10: 1269.
https://doi.org/10.3390/e23101269