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arXiv · 2502.02375

A Compact theorem on the compactness of ultra-compact objects with monotonically decreasing matter fields

Shahar Hod
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Abstract

Self-gravitating horizonless ultra-compact objects that possess light rings have attracted the attention of physicists and mathematicians in recent years. In the present compact paper we raise the following physically interesting question: Is there a lower bound on the global compactness parameters ${\cal C}\equiv\text{max}_r\{2m(r)/r\}$ of spherically symmetric ultra-compact objects? Using the non-linearly coupled Einstein-matter field equations we explicitly prove that spatially regular ultra-compact objects with monotonically decreasing density functions (or monotonically decreasing radial pressure functions) are characterized by the lower bound ${\cal C}\geq1/3$ on their dimensionless compactness parameters.

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Shahar Hod. 2025-02-04. A Compact theorem on the compactness of ultra-compact objects with monotonically decreasing matter fields. https://arxiv.org/abs/2502.02375

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