# Weak Deflection Angle and Greybody Bound of Magnetized Regular Black Hole

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## Abstract

**:**

## 1. Introduction

## 2. Magnetized Regular Black Hole (MRBH)

## 3. Weak Deflection Angle for MRBH in Non-Plasma Medium

## 4. Graphical Representation for Non-Plasma of MRBH

#### 4.1. Angle of Deflection $\gamma $ versus Impact Parameter b

#### 4.2. Deflection Angle $\gamma $ versus BH Charge q

## 5. Effect of Plasma on Weak Deflection Angle $\mathbf{\gamma}$ for MRBH

## 6. Graphical Analysis for Plasma Medium

#### 6.1. Deflection Angle $\gamma $ with Impact Parameter b

#### 6.2. Deflection Angle $\gamma $ with BH Charge q

## 7. Derivation of Greybody Factor of MRBH

## 8. Graphical Study of the Greybody Bound for MRBH

#### Rigorous Bound ${T}_{b}$ in Connection with Omega $\omega $

## 9. Conclusions

#### 9.1. Bending Angle $\gamma $

- (i)
- Non-plasma Medium:The deflection angle $\gamma $ obtained in Equation (19) for non-plasma medium depends on m of the BH, q, b, G, and l. We observe that in the attain deflection angle, the first term is the well-known result for the Schwarzschild black hole, when we put $G=1$, $l=0$, and $q=0$.
- (ii)
- Plasma Medium:In case the of the plasma medium, the deflection angle $\gamma $ in Equation (28) depends on m of the BH, q, b, G, and l and on the plasma term. The bending angle obtained in the plasma medium increases with the parameter $\frac{{\omega}_{e}^{2}}{{\omega}_{\infty}^{2}}$, which shows that the lower the photon frequency observed by a static spectator at infinity, the greater the deflection angle of it for the fixed electron plasma frequency. We also observe that, when we take the $q=0$, $G=1$, and $l=0$, the deflection angle obtained in the plasma medium reduces to the deflection angle of the Schwarzschild BH in plasma medium. We also found that the deflection angle obtained in the plasma medium reduces to the deflection angle that we obtained in case of non-plasma, when we take $\frac{{\omega}_{e}^{2}}{{\omega}_{\infty}^{2}}=0$.

#### 9.2. Greybody Factor Bounds T

#### 9.3. Graphical Behaviour

- (i)
- For MRBH:
**The bending angle $\gamma $ versus impact parameter b**: The graphical behaviour shows that, when we fix the value of $m=1$, $l=0.5$, and $G=1$, and give variation to q, the deflection angle shows positive behaviour for $0.6<q<2.09$ and shows negative behaviour at $q=0.6$ and $q=2.09$. Similarly, we observed that the deflection angle is decreasing and eventually goes to infinity for large values of l, and by fixing $m=1$, $q=0.8$, and Newton’s constant $G=1$.**Bending angle $\gamma $ versus magnetic charge q**: For the fixed values of $G=1$, $m=1$, and $l=0.5$, the $\gamma $ angle first increases for small values of b, but for large values of b, the deflection angle decreases.

#### 9.4. Graphical Analysis of Greybody Bound

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

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Javed, W.; Riaz, S.; Övgün, A.
Weak Deflection Angle and Greybody Bound of Magnetized Regular Black Hole. *Universe* **2022**, *8*, 262.
https://doi.org/10.3390/universe8050262

**AMA Style**

Javed W, Riaz S, Övgün A.
Weak Deflection Angle and Greybody Bound of Magnetized Regular Black Hole. *Universe*. 2022; 8(5):262.
https://doi.org/10.3390/universe8050262

**Chicago/Turabian Style**

Javed, Wajiha, Sibgha Riaz, and Ali Övgün.
2022. "Weak Deflection Angle and Greybody Bound of Magnetized Regular Black Hole" *Universe* 8, no. 5: 262.
https://doi.org/10.3390/universe8050262