Lower bound on the compactness of isotropic ultracompact objects

Horizonless spacetimes describing spatially regular ultracompact 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 ultracompact object? Using analytical techniques, we prove that ultracompact isotropic matter configurations with light rings are characterized by the dimensionless lower bound ${\max }_r\{2m(r)/r\}>7/12$ on their global compactness parameter.