https://doi.org/10.1140/epjc/s10052-025-13866-y
Regular Article - Theoretical Physics
A compact theorem on the compactness of ultra-compact objects with monotonically decreasing matter fields
1
The Ruppin Academic Center, 40250, Emeq Hefer, Israel
2
The Hadassah Academic College, 91010, Jerusalem, Israel
Received:
30
December
2024
Accepted:
19
January
2025
Published online:
3
February
2025
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 
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 
on their dimensionless compactness parameters.
© The Author(s) 2025
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