Lower bound on the compactness of isotropic ultra-compact objects

Horizonless spacetimes describing spatially regular ultra-compact objects which, like black-hole spacetimes, possess closed null circular geodesics (light rings) have recently attracted much attention from physicists and mathematicians. In the present paper we raise the following physically intriguing question: How compact is an ultra-compact object? Using analytical techniques, we prove that ultra-compact isotropic matter configurations with light rings are characterized by the dimensionless lower bound ${\text{max}}_r\{2m(r)\mathrm{/}r\}>7\mathrm{/}12$ on their global compactness parameter.