# Gravitational Condensate Stars: An Alternative to Black Holes

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction 1

## 2. Solution of Einstein Equations for Static, Spherical Symmetry

## 3. Stability

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Notes

1 | The main text of this paper is a minimally corrected version of the previously unpublished arXiv submission [1],
in which the original proposal that the final state of complete gravitational collapse is a non-singular gravitational vacuum
condensate star (‘gravastar’) was made. A somewhat expanded version of this paper appeared in [2].
The authors take this opportunity to provide an extended Appendix A, updating the status of the gravastar proposal, collecting
under seven subtitles the most significant developments over the past two decades relating to this proposal, with additional
explanation and annotations for each. |

2 | The sign conventions in [1,2] are such that ${\sigma}_{1,2}$ there are the negative of the surface stress tensors ${\mathcal{S}}_{\theta}^{\phantom{\rule{4pt}{0ex}}\theta}={\mathcal{S}}_{\varphi}^{\phantom{\rule{4pt}{0ex}}\varphi}$ properly defined here. Equations (C5) and (C7) of [19] also have an overall sign change from the Lanczos–Israel formula (C5) for ${\mathcal{S}}_{a}^{\phantom{\rule{4pt}{0ex}}b}$, such that $\eta ,\sigma $ of (C7) in [19] have the same values as $\eta ,\sigma $ in [1,2]. |

## Appendix A. Gravitational Condensate Stars: Further Developments

#### Appendix A.1. Background: Preliminary Description the Boundary Layer

#### Appendix A.2. The Macroscopic Effects of the Conformal Anomaly and Value of ε

#### Appendix A.3. The Schwarzschild Interior Solution and Determination of C

#### Appendix A.4. Thin Shell vs. Thick Shell

#### Appendix A.5. The Status of Constraints from Astronomical Observations

#### Appendix A.6. Gravitational Waves and Echoes

#### Appendix A.7. The EFT of Gravity and Dynamical Vacuum Energy

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**MDPI and ACS Style**

Mazur, P.O.; Mottola, E.
Gravitational Condensate Stars: An Alternative to Black Holes. *Universe* **2023**, *9*, 88.
https://doi.org/10.3390/universe9020088

**AMA Style**

Mazur PO, Mottola E.
Gravitational Condensate Stars: An Alternative to Black Holes. *Universe*. 2023; 9(2):88.
https://doi.org/10.3390/universe9020088

**Chicago/Turabian Style**

Mazur, Pawel O., and Emil Mottola.
2023. "Gravitational Condensate Stars: An Alternative to Black Holes" *Universe* 9, no. 2: 88.
https://doi.org/10.3390/universe9020088