# The Symmetry of the Interior and Exterior of Schwarzschild and Reissner–Nordstrom Black Holes—Sphere vs. Cylinder

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## Abstract

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## 1. Introduction

## 2. A Simple Example–Free Fall Descriptions in Different Coordinate Systems

## 3. Expanding and Contracting Interior of Schwarzschild and Reissner–Nordström Black Holes

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The dynamical expansion/contraction of the interior of a Schwarzschild black hole: inside the horizon, $r<{r}_{S}$ the space has a cigar-like shape with a sphere as its basis perpendicular to the homogeneity t-axis. It is expanding along the t-direction, i.e., every pair of two fixed points A and B are carried away at an increasing rate and contracting perpendicularly to this direction as the radius $r$ of the sphere diminishes to zero.

**Figure 2.**The dynamical expansion followed by contraction (t-axis) of the interior of a Reissner–Nordström black hole: inside the horizon, ${r}_{-}<r<{r}_{+}$. The space has a cigar-like shape with a sphere as its basis perpendicular to the homogeneity t-axis. It first expands along the t-direction until the instant $r={r}_{min}$, when it then starts contracting; contraction terminates at the endpoint $r={r}_{-},$ when the t-axis is compressed to a point.

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**MDPI and ACS Style**

Augousti, A.T.; Radosz, A.; Gusin, P.; Kaczmarek, A.
The Symmetry of the Interior and Exterior of Schwarzschild and Reissner–Nordstrom Black Holes—Sphere vs. Cylinder. *Symmetry* **2020**, *12*, 859.
https://doi.org/10.3390/sym12050859

**AMA Style**

Augousti AT, Radosz A, Gusin P, Kaczmarek A.
The Symmetry of the Interior and Exterior of Schwarzschild and Reissner–Nordstrom Black Holes—Sphere vs. Cylinder. *Symmetry*. 2020; 12(5):859.
https://doi.org/10.3390/sym12050859

**Chicago/Turabian Style**

Augousti, Andy T., Andrzej Radosz, Pawel Gusin, and Aleksander Kaczmarek.
2020. "The Symmetry of the Interior and Exterior of Schwarzschild and Reissner–Nordstrom Black Holes—Sphere vs. Cylinder" *Symmetry* 12, no. 5: 859.
https://doi.org/10.3390/sym12050859