A compact theorem on the compactness of ultra-compact objects with monotonically decreasing matter fields
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 pa...
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-02-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-025-13866-y |
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| Summary: | 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 $$\mathcal{C}\equiv \text {max}_r\{2m(r)/r\}$$ C ≡ max r { 2 m ( 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 $$\mathcal{C}\ge 1/3$$ C ≥ 1 / 3 on their dimensionless compactness parameters. |
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| ISSN: | 1434-6052 |