# Shadow Images of a Rotating Dyonic Black Hole with a Global Monopole Surrounded by Perfect Fluid

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## Abstract

**:**

## 1. Introduction

## 2. An SDBH with a Global Monopole in Perfect Fluid

## 3. An RDBH with a Global Monopole in Perfect Fluid

#### 3.1. Surface Topology

**Theorem**

**1.**

#### 3.2. Shape of Ergoregion

## 4. Null Geodesics

**On****Left****Side**- $\mathcal{J}$ is the Jacobi action, defined as the function of affine parameter $\tau $ and coordinates ${x}^{\mu}$ i.e., $\mathcal{J}=\mathcal{J}(\tau ,{x}^{\mu})$.
**On****Right Side**- $\mathcal{H}$ is the Hamiltonian of test particle’s motion and is equivalent to ${g}^{\mu \nu}{\partial}_{\mu}\mathcal{J}\phantom{\rule{0.277778em}{0ex}}{\partial}_{\nu}\mathcal{J}$.

## 5. Circular Orbits

## 6. Silhoutte of Black Holes

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Plots showing the shape of ergoregion in $xz$-plane for different values of a, $\omega $, and $\upsilon $. We have chosen ${Q}_{E}={Q}_{M}=0.1$ in all plots. The blue and the red lines correspond to horizons and static limit surfaces, respectively. The outer red line corresponds to the static limit surface, whereas the two blue lines correspond to the two horizons. Due to the small values of $\upsilon $ and a arbitrary value of a we observe almost indistinguishable plots for the shape of the ergoregion.

**Figure 2.**The effective potential of photon moving in equatorial plane, with respect to its radial motion: $\omega =1/3$ for radiation, $\omega =0$ for dust and $\omega =-1/3$ for dark matter.

**Figure 3.**Variation in shape of a rotating dyonic global monopole surrounded by a perfect fluid. Magnetic and electric charges are kept constant such that ${Q}_{E}={10}^{-2}={Q}_{M}$. In each graph the Kerr case, that is, $\gamma =0$ and $\upsilon =0$, is represented by a solid line, $\gamma =0.05$ by dotdashed and $\gamma =0.08$ by dashed lines. For dark matter $(\omega =-1/3)$ and dust $(\omega =0)$ case $\upsilon =0.01$, whereas $\upsilon =-0.01$ in the case of radiation $(\omega =1/3)$.

**Figure 4.**Variation in the shape of a rotating dyonic black hole with global monopole surrounded by a perfect fluid, for different values of perfect fluid parameter $\upsilon $. Magnetic and electric charges along with the global monopole parameter are kept constant such that ${Q}_{E}={10}^{-2}={Q}_{M}$ and $\gamma =0.08$. For dark matter and dust case $\upsilon =0$ (Solid), $0.05$ (DotDashed) and $0.1$ (Dashed). In the case of radiation $\upsilon =0$ (Solid), $-0.01$ (DotDashed) and $-0.05$ (Dashed).

**Figure 6.**The figure shows the energy emission rate when $a=0.46$ (

**upper panel**) and $a=0.92$ (

**lower panel**).

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Haroon, S.; Jusufi, K.; Jamil, M.
Shadow Images of a Rotating Dyonic Black Hole with a Global Monopole Surrounded by Perfect Fluid. *Universe* **2020**, *6*, 23.
https://doi.org/10.3390/universe6020023

**AMA Style**

Haroon S, Jusufi K, Jamil M.
Shadow Images of a Rotating Dyonic Black Hole with a Global Monopole Surrounded by Perfect Fluid. *Universe*. 2020; 6(2):23.
https://doi.org/10.3390/universe6020023

**Chicago/Turabian Style**

Haroon, Sumarna, Kimet Jusufi, and Mubasher Jamil.
2020. "Shadow Images of a Rotating Dyonic Black Hole with a Global Monopole Surrounded by Perfect Fluid" *Universe* 6, no. 2: 23.
https://doi.org/10.3390/universe6020023