Geometrical origin for the compaction function for primordial black hole formation

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Summary

The Shibata-Sasaki compaction function is reinterpreted as the compactness of an unphysical static spacetime, providing a geometrical origin for its ability to indicate primordial black hole formation.

Highlights

• The Shibata-Sasaki compaction function is reexamined in the context of primordial black hole formation.
• A conformal transformation is used to relate the physical spacetime to an unphysical static spacetime.
• The compactness of the unphysical spacetime is identified as the Shibata-Sasaki compaction function in the long-wavelength limit.
• The Shibata-Sasaki compaction function is bounded by 1/2, corresponding to an extremal surface in the unphysical spacetime.
• The extremal surface is shown to be a photon sphere, which is stable or unstable depending on the configuration.
• The stability of the photon sphere is related to the type of perturbation, with type II perturbations admitting stable photon spheres.
• The results provide a new understanding of the Shibata-Sasaki compaction function and its role in primordial black hole formation.

Key Insights

• The Shibata-Sasaki compaction function can be understood as a measure of the compactness of an unphysical static spacetime, providing a geometrical origin for its ability to indicate primordial black hole formation.
• The compactness of the unphysical spacetime is a key factor in determining the formation of primordial black holes, with a value of 1/2 corresponding to an extremal surface.
• The extremal surface is a photon sphere, which is a critical component in the formation of primordial black holes.
• The stability of the photon sphere is dependent on the type of perturbation, with type II perturbations admitting stable photon spheres.
• The results provide a new understanding of the Shibata-Sasaki compaction function and its role in primordial black hole formation, highlighting the importance of geometrical considerations in this context.
• The use of a conformal transformation to relate the physical spacetime to an unphysical static spacetime is a key aspect of this work, allowing for a deeper understanding of the Shibata-Sasaki compaction function.
• The findings of this study have implications for our understanding of primordial black hole formation and the role of the Shibata-Sasaki compaction function in this process.

Mindmap

Citation

Harada, T., Iizuka, H., Koga, Y., & Yoo, C.-M. (2024). Geometrical origin for the compaction function for primordial black hole formation (Version 2). arXiv. https://doi.org/10.48550/ARXIV.2409.05544