# Higher Dimensional Rotating Black Hole Solutions in Quadratic f(R) Gravitational Theory and the Conserved Quantities

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## Abstract

**:**

## 1. Introduction

## 2. Basics of $f\left(R\right)$ Gravitational Theory

**$N>4$**, and its solution takes the form

## 3. Rotating Black **Hole** Solutions

## 4. Total Conserved Charge

## 5. Regularization with Relocalization for the Conserved Charge

## 6. Thermodynamics for Black Holes

## 7. Summary and Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Symbols Used in the Calculations of Conserved Quantities

## Appendix B. Non-Zero Components for the Christoffel Symbols of the Second Kind and Ricci Curvature Tensor

## References

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**Figure 1.**The function h(r) vs. the radial coordinate r for (

**a**) N = 4, ${c}_{1}=-1$. (

**b**) N = 5, ${c}_{2}=-1$ (all of the figures are reproduced using the Maple software 16).

**Figure 2.**Horizon ${r}_{h}$ vs. (

**a**,

**d**) Hawking temperature (

**b**,

**e**); entropy (

**c**,

**f**) heat capacity for the four-dimensional and five-dimensional cases, respectively. In these figures, we take $b=0.1$ when $N=4$ and $b=0.01$ when $N=5$.

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Nashed, G.G.L.; Bamba, K.
Higher Dimensional Rotating Black Hole Solutions in Quadratic *f*(*R*) Gravitational Theory and the Conserved Quantities. *Entropy* **2021**, *23*, 358.
https://doi.org/10.3390/e23030358

**AMA Style**

Nashed GGL, Bamba K.
Higher Dimensional Rotating Black Hole Solutions in Quadratic *f*(*R*) Gravitational Theory and the Conserved Quantities. *Entropy*. 2021; 23(3):358.
https://doi.org/10.3390/e23030358

**Chicago/Turabian Style**

Nashed, Gamal G. L., and Kazuharu Bamba.
2021. "Higher Dimensional Rotating Black Hole Solutions in Quadratic *f*(*R*) Gravitational Theory and the Conserved Quantities" *Entropy* 23, no. 3: 358.
https://doi.org/10.3390/e23030358