A compact theorem on the compactness of ultra-compact objects with monotonically decreasing matter fields - Shahar Hod (European Physical Journal C: Particles and 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 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.