# Yukawa–Casimir Wormholes in f(Q) Gravity

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Symmetric Teleparallel Gravity i.e., $\mathit{f}\left(\mathit{Q}\right)$-Gravity

## 3. Wormhole Geometry and Solution of Field Equations in $\mathit{f}\left(\mathit{Q}\right)$ Gravity

#### The Energy Conditions

## 4. The Yukawa–Casimir Wormhole Model

#### 4.1. Linear Form: $f\left(Q\right)=\alpha Q$

#### 4.2. Power Law Form: $f\left(Q\right)=\alpha {Q}^{2}+\beta $

#### 4.3. Quadratic Form: $f\left(Q\right)=\alpha {Q}^{2}+\beta Q+\gamma $

#### 4.4. Inverse Power Law Form: $f\left(Q\right)=Q+\frac{\alpha}{Q}$

## 5. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

#### Appendix A.1. Linear Form: f(Q) = αQ

#### Appendix A.2. Power Law Form: f(Q) = αQ^{2} + β

#### Appendix A.3. Quadratic Form: f(Q) = αQ^{2} + βQ + γ

#### Appendix A.4. Inverse Power Law Form: f(Q) = Q + $\frac{\alpha}{Q}$

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**Figure 1.**Plots: (

**a**) Energy density ($\rho $) and (

**b**) Radial NEC ($\rho +{p}_{r}$) with throat radius ${r}_{0}=1$ and $\alpha =1$ in $f\left(Q\right)=\alpha Q$ gravity.

**Figure 2.**Plots: (

**a**) Tangential NEC ($\rho +{p}_{t}$) and (

**b**) SEC ($\rho +{p}_{r}+2{p}_{t}$) with throat radius ${r}_{0}=1$ and $\alpha =1$ in $f\left(Q\right)=\alpha Q$ gravity.

**Figure 3.**Plots: (

**a**) Radial DEC ($\rho -|{p}_{r}\left|\right)$ and (

**b**) Tangential DEC ($\rho -|{p}_{t}|$) with throat radius ${r}_{0}=1$ and $\alpha =1$ in $f\left(Q\right)=\alpha Q$ gravity.

**Figure 4.**Plots: (

**a**) Energy density ($\rho $) and (

**b**) radial NEC ($\rho +{p}_{r}$) with throat radius ${r}_{0}=1$, $\alpha =1$, and $\beta =2$ in $f\left(Q\right)=\alpha {Q}^{2}+\beta $ gravity.

**Figure 5.**Plots: (

**a**) Tangential NEC ($\rho +{p}_{t}$) and (

**b**) SEC ($\rho +{p}_{r}+2{p}_{t}$) with throat radius ${r}_{0}=1$, $\alpha =1$, and $\beta =2$ in $f\left(Q\right)=\alpha {Q}^{2}+\beta $ gravity.

**Figure 6.**Plots: (

**a**) Radial DEC ($\rho -|{p}_{r}\left|\right)$, and (

**b**) Tangential DEC ($\rho -|{p}_{t}|$) with throat radius ${r}_{0}=1$, $\alpha =1$, and $\beta =2$ in $f\left(Q\right)=\alpha {Q}^{2}+\beta $ gravity.

**Figure 7.**Plots: (

**a**) Energy density ($\rho $) and (

**b**) Radial NEC ($\rho +{p}_{r}$) with throat radius ${r}_{0}=1$, $\alpha =1$, $\beta =1$, and $\gamma =2$ in $f\left(Q\right)=\alpha {Q}^{2}+\beta Q+\gamma $ gravity.

**Figure 8.**Plots: (

**a**) Tangential NEC ($\rho +{p}_{t}$) and (

**b**) SEC ($\rho +{p}_{r}+2{p}_{t}$) with throat radius ${r}_{0}=1$, $\alpha =1$, $\beta =1$, and $\gamma =2$ in $f\left(Q\right)=\alpha {Q}^{2}+\beta Q+\gamma $ gravity.

**Figure 9.**Plots: (

**a**) Radial DEC ($\rho -|{p}_{r}\left|\right)$, and (

**b**) Tangential DEC ($\rho -|{p}_{t}|$) with throat radius ${r}_{0}=1$, $\alpha =1$, $\beta =1$, and $\gamma =2$ in $f\left(Q\right)=\alpha {Q}^{2}+\beta Q+\gamma $ gravity.

**Figure 10.**Plots: (

**a**) Energy density ($\rho $) and (

**b**) Radial NEC ($\rho +{p}_{r}$) with throat radius ${r}_{0}=1$ and $\alpha =-0.1$ in $f\left(Q\right)=Q+\frac{\alpha}{Q}$ gravity.

**Figure 11.**Plots: (

**a**) Tangential NEC ($\rho +{p}_{t}$) and (

**b**) SEC ($\rho +{p}_{r}+2{p}_{t}$) with throat radius ${r}_{0}=1$ and $\alpha =-0.1$ in $f\left(Q\right)=Q+\frac{\alpha}{Q}$ gravity.

**Figure 12.**Plots: (

**a**) Radial DEC ($\rho -|{p}_{r}\left|\right)$, and (

**b**) Tangential DEC ($\rho -|{p}_{t}|$) with throat radius ${r}_{0}=1$ and $\alpha =-0.1$ in $f\left(Q\right)=Q+\frac{\alpha}{Q}$ gravity.

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**MDPI and ACS Style**

Mishra, A.K.; Shweta; Sharma, U.K. Yukawa–Casimir Wormholes in *f*(*Q*) Gravity. *Universe* **2023**, *9*, 161.
https://doi.org/10.3390/universe9040161

**AMA Style**

Mishra AK, Shweta, Sharma UK. Yukawa–Casimir Wormholes in *f*(*Q*) Gravity. *Universe*. 2023; 9(4):161.
https://doi.org/10.3390/universe9040161

**Chicago/Turabian Style**

Mishra, Ambuj Kumar, Shweta, and Umesh Kumar Sharma. 2023. "Yukawa–Casimir Wormholes in *f*(*Q*) Gravity" *Universe* 9, no. 4: 161.
https://doi.org/10.3390/universe9040161