# Towards Quantum Simulation of Black Holes in a dc-SQUID Array

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## Abstract

**:**

## 1. Introduction

## 2. Model and Results

#### 2.1. Simulator

#### 2.2. Black Holes

## 3. Results

#### 3.1. Schwarzschild

#### 3.2. Reissner–Nordstrøm

- If $A=0$:

- 2.
- If $0<\left|A\right|<\frac{1}{\sqrt{2}}$:

- 3
- If $\frac{1}{\sqrt{2}}\le \left|A\right|<1$:

- 4
- If $\left|A\right|=1$:

#### 3.3. Kerr

#### 3.4. Kerr–Newman

## 4. Summary and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**External magnetic flux $\pi {\varphi}_{\mathrm{ext}}/{\varphi}_{0}$ versus the adimensional distance $\xi =r/M$ for the simulation of a Schwarzschild black hole. The dashed line represents the threshold value $\pi {\varphi}_{\mathrm{ext}}/{\varphi}_{0}=\pi /2$.

**Figure 2.**Effective speed of light squared ${\tilde{c}}^{2}$ versus the adimensional distance $\xi =r/M$ for the simulation of a Schwarzschild black hole.

**Figure 3.**External magnetic flux $\pi {\varphi}_{\mathrm{ext}}/{\varphi}_{0}$ versus the adimensional distance $\xi =r/M$ for the simulation of a Reissner–Nordstrøm black hole, for different values of $A=Q/M$. The dashed line represents the threshold value $\pi {\varphi}_{\mathrm{ext}}/{\varphi}_{0}=\pi /2$.

**Figure 4.**External magnetic flux $\pi {\varphi}_{\mathrm{ext}}/{\varphi}_{0}$ versus the adimensional distance $\xi =r/M$ for the simulation of a Kerr black hole with fixed $\theta =0$, and for different values of $B=S/{M}^{2}$. The dashed line represents the threshold value $\pi {\varphi}_{\mathrm{ext}}/{\varphi}_{0}=\pi /2$.

**Figure 5.**External magnetic flux $\pi {\varphi}_{\mathrm{ext}}/{\varphi}_{0}$ versus the adimensional distance $\xi =r/M$ for the simulation of a Kerr black hole with fixed $\theta =\pi /4$, and for different values of $B=S/{M}^{2}$. The dashed line represents the threshold value $\pi {\varphi}_{\mathrm{ext}}/{\varphi}_{0}=\pi /2$.

**Figure 6.**A zoom-in of Figure 5, where the regions with $\pi {\varphi}_{\mathrm{ext}}/{\varphi}_{0}$ above the threshold value $\pi /2$ (dashed line) can be better appreciated.

**Figure 7.**External magnetic flux $\pi {\varphi}_{\mathrm{ext}}/{\varphi}_{0}$ versus the adimensional distance $\xi =r/M$ for the simulation of a Kerr black hole with fixed $\theta =\pi /2$, and for different values of $B=S/{M}^{2}$. The dashed line represents the threshold value $\pi {\varphi}_{\mathrm{ext}}/{\varphi}_{0}=\pi /2$.

**Figure 8.**External magnetic flux $\pi {\varphi}_{\mathrm{ext}}/{\varphi}_{0}$ versus the adimensional distance $\xi =r/M$ for the simulation of a Kerr–Newman black hole with fixed $\theta =0$ and $A=Q/M=0.7$, and for different values of $B=S/{M}^{2}$. The dashed line represents the threshold value $\pi {\varphi}_{\mathrm{ext}}/{\varphi}_{0}=\pi /2$.

**Figure 9.**External magnetic flux $\pi {\varphi}_{\mathrm{ext}}/{\varphi}_{0}$ versus the adimensional distance $\xi =r/M$ for the simulation of a Kerr–Newman black hole with fixed $\theta =0$ and $A=Q/M=0.71$, and for different values of $B=S/{M}^{2}$. The dashed line represents the threshold value $\pi {\varphi}_{\mathrm{ext}}/{\varphi}_{0}=\pi /2$.

**Figure 10.**External magnetic flux $\pi {\varphi}_{\mathrm{ext}}/{\varphi}_{0}$ versus the adimensional distance $\xi =r/M$ for the simulation of a Kerr–Newman black hole with fixed $\theta =\pi /4$ and $A=Q/M=0.7$, and for different values of $B=S/{M}^{2}$. The dashed line represents the threshold value $\pi {\varphi}_{\mathrm{ext}}/{\varphi}_{0}=\pi /2$.

**Figure 11.**External magnetic flux $\pi {\varphi}_{\mathrm{ext}}/{\varphi}_{0}$ versus the adimensional distance $\xi =r/M$ for the simulation of a Kerr–Newman black hole with fixed $\theta =\pi /4$ and $A=Q/M=0.71$, and for different values of $B=S/{M}^{2}$. The dashed line represents the threshold value $\pi {\varphi}_{\mathrm{ext}}/{\varphi}_{0}=\pi /2$.

**Figure 12.**External magnetic flux $\pi {\varphi}_{\mathrm{ext}}/{\varphi}_{0}$ versus the adimensional distance $\xi =r/M$ for the simulation of a Kerr–Newman black hole with fixed $\theta =\pi /2$ and $A=Q/M=0.7$, and for different values of $B=S/{M}^{2}$. The dashed line represents the threshold value $\pi {\varphi}_{\mathrm{ext}}/{\varphi}_{0}=\pi /2$.

**Figure 13.**External magnetic flux $\pi {\varphi}_{\mathrm{ext}}/{\varphi}_{0}$ versus the adimensional distance $\xi =r/M$ for the simulation of a Kerr–Newman black hole with fixed $\theta =\pi /2$ and $A=Q/M=0.71$, and for different values of $B=S/{M}^{2}$. The dashed line represents the threshold value $\pi {\varphi}_{\mathrm{ext}}/{\varphi}_{0}=\pi /2$.

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**MDPI and ACS Style**

Terrones, A.; Sabín, C.
Towards Quantum Simulation of Black Holes in a dc-SQUID Array. *Universe* **2021**, *7*, 499.
https://doi.org/10.3390/universe7120499

**AMA Style**

Terrones A, Sabín C.
Towards Quantum Simulation of Black Holes in a dc-SQUID Array. *Universe*. 2021; 7(12):499.
https://doi.org/10.3390/universe7120499

**Chicago/Turabian Style**

Terrones, Adrián, and Carlos Sabín.
2021. "Towards Quantum Simulation of Black Holes in a dc-SQUID Array" *Universe* 7, no. 12: 499.
https://doi.org/10.3390/universe7120499